{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>InvoiceNo</th>\n",
       "      <th>StockCode</th>\n",
       "      <th>Description</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>InvoiceDate</th>\n",
       "      <th>UnitPrice</th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>536365</td>\n",
       "      <td>85123A</td>\n",
       "      <td>WHITE HANGING HEART T-LIGHT HOLDER</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.55</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>536365</td>\n",
       "      <td>71053</td>\n",
       "      <td>WHITE METAL LANTERN</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>536365</td>\n",
       "      <td>84406B</td>\n",
       "      <td>CREAM CUPID HEARTS COAT HANGER</td>\n",
       "      <td>8</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>2.75</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029G</td>\n",
       "      <td>KNITTED UNION FLAG HOT WATER BOTTLE</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>536365</td>\n",
       "      <td>84029E</td>\n",
       "      <td>RED WOOLLY HOTTIE WHITE HEART.</td>\n",
       "      <td>6</td>\n",
       "      <td>2010-12-01 08:26:00</td>\n",
       "      <td>3.39</td>\n",
       "      <td>17850.0</td>\n",
       "      <td>United Kingdom</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  InvoiceNo StockCode                          Description  Quantity  \\\n",
       "0    536365    85123A   WHITE HANGING HEART T-LIGHT HOLDER         6   \n",
       "1    536365     71053                  WHITE METAL LANTERN         6   \n",
       "2    536365    84406B       CREAM CUPID HEARTS COAT HANGER         8   \n",
       "3    536365    84029G  KNITTED UNION FLAG HOT WATER BOTTLE         6   \n",
       "4    536365    84029E       RED WOOLLY HOTTIE WHITE HEART.         6   \n",
       "\n",
       "          InvoiceDate  UnitPrice  CustomerID         Country  \n",
       "0 2010-12-01 08:26:00       2.55     17850.0  United Kingdom  \n",
       "1 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  \n",
       "2 2010-12-01 08:26:00       2.75     17850.0  United Kingdom  \n",
       "3 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  \n",
       "4 2010-12-01 08:26:00       3.39     17850.0  United Kingdom  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "df = pd.read_excel(\"Online_Retail.xlsx\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set_palette(\"husl\")\n",
    "sns.set(rc={'image.cmap': 'coolwarm'})\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime as dt\n",
    "df['InvoiceDate'] = pd.to_datetime(df['InvoiceDate']).dt.date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[pd.notnull(df['CustomerID'])]\n",
    "df = df[(df['Quantity']>0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Sales'] = df['Quantity'] * df['UnitPrice']\n",
    "cols_of_interest = ['CustomerID', 'InvoiceDate', 'Sales']\n",
    "df = df[cols_of_interest]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   CustomerID InvoiceDate  Sales\n",
      "0     17850.0  2010-12-01  15.30\n",
      "1     17850.0  2010-12-01  20.34\n",
      "2     17850.0  2010-12-01  22.00\n",
      "3     17850.0  2010-12-01  20.34\n",
      "4     17850.0  2010-12-01  20.34\n",
      "4339\n"
     ]
    }
   ],
   "source": [
    "print(df.head())\n",
    "print(df['CustomerID'].nunique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12346.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>325.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12347.0</th>\n",
       "      <td>6.0</td>\n",
       "      <td>365.0</td>\n",
       "      <td>367.0</td>\n",
       "      <td>599.701667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12348.0</th>\n",
       "      <td>3.0</td>\n",
       "      <td>283.0</td>\n",
       "      <td>358.0</td>\n",
       "      <td>301.480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12349.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12350.0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>310.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value\n",
       "CustomerID                                           \n",
       "12346.0           0.0      0.0  325.0        0.000000\n",
       "12347.0           6.0    365.0  367.0      599.701667\n",
       "12348.0           3.0    283.0  358.0      301.480000\n",
       "12349.0           0.0      0.0   18.0        0.000000\n",
       "12350.0           0.0      0.0  310.0        0.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lifetimes.plotting import *\n",
    "from lifetimes.utils import *\n",
    "from lifetimes.estimation import *\n",
    "\n",
    "data = summary_data_from_transaction_data(df, 'CustomerID', 'InvoiceDate', monetary_value_col='Sales', observation_period_end='2011-12-9')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    4339.000000\n",
      "mean        2.864024\n",
      "std         5.952745\n",
      "min         0.000000\n",
      "25%         0.000000\n",
      "50%         1.000000\n",
      "75%         3.000000\n",
      "max       131.000000\n",
      "Name: frequency, dtype: float64\n",
      "0.3569946992394561\n"
     ]
    },
    {
     "data": {
      "image/png": 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BSJKKLAhJUpEFIUkqsiAkSUUWhCSpyIKQJBVZEJKkIgtCklRkQUiSiiwISVKRBSFJKrIg\nJElFFoQkqajnHzkaEbcBP63v3gt8EvgIsAvYmJl/FRHDwMeAZwOPAG/JzLt6nVWS5rOeFkREHA6Q\nmUs7xm4HXgvcA3w5IhYBxwKHZ+YLIuIE4CJgeS+zStJ81+stiGcDCyNiY/211wCHZebdABFxI/AS\n4LeAGwAy8+sR8dx9vfDY2EJGRhY0lXsv4+OjPfta+zJIWfZHW3NDe7O3NTe0N3tbc0PvC+Ih4EPA\nZcBvAxuAnR2PTwBPB47gsd1QALsjYiQzd830wjt2PDT3aWexbdtET7/eTMbHRwcmy/5oa25ob/a2\n5ob2Zm9D7tkKrNcFsRW4KzMnga0R8VPg8R2Pj1IVxsL69pTh2cpBkjT3en0U09lU6wlExJOpiuBn\nEfGMiBgClgGbgS3AK+p5JwDf6nFOSZr3er0F8U/A5RHxVWCSqjD2AJ8DFlAdxfSNiPgv4KUR8TVg\nCDirxzklad7raUFk5qPAHxceOmHavD3A23oSSpJU5IlykqQiC0KSVGRBSJKKLAhJUpEFIUkqsiAk\nSUUWhCSpyIKQJBVZEJKkIgtCklRkQUiSiiwISVKRBSFJKrIgJElFvf48iIPG2R+8qTi+/j0v7nES\nSWqGWxCSpCILQpJUZEFIkoosCElSkYvUc8zFa0kHC7cgJElFFoQkqciCkCQVWRCSpCIXqXvExWtJ\nbeMWhCSpyIKQJBUN7C6miBgGPgY8G3gEeEtm3tXfVHNvpl1PM3GXlKReGdiCAF4NHJ6ZL4iIE4CL\ngOV9ztR3rmVI6pVBLoiTgBsAMvPrEfHcPucZaPu7JTKbmcrGcpLml6HJycl+ZyiKiMuAqzNzQ33/\nPuDpmbmrv8kkaX4Y5EXqB4DRjvvDloMk9c4gF8QW4BUA9RrEt/obR5Lml0Feg7gGeGlEfA0YAs7q\ncx5JmlcGdg1CktRfg7yLSZLURxaEJKnIgpAkFQ3yInXj2nY5j4g4BFgPHAscBnwA+A5wOTAJ3AGs\nyMw9fYo4q4h4InAr8FJgF+3J/V7gD4BDqX5eNjHg2euflU9T/azsBt5KC77nEbEYuDAzl0bEcRTy\nRsRq4DSq97MyM2/pW+DatNzPAT5K9X1/BHhTZv44It4K/ClV7g9k5vX9S9yd+b4F8cvLeQDvobqc\nxyA7E9iemScDpwKXAGuBVfXYEAN6OZL6P6xPAg/XQ23JvRQ4EXghsAQ4mnZkfwUwkpknAn8N/A0D\nnjsi3g1cBhxeD+2VNyIWUf09LAbOAC7tR9ZOhdwfAd6RmUuBLwLnR8STgHdS/RwtA/4uIg7rQ9z9\nMt8L4lcu5wEM+uU8rgQu6Li/Czie6jdagA3AKb0O1aUPAZ8A/re+35bcy6jOwbkGuA64nnZk3wqM\n1FvJRwC/YPBz3w28puN+Ke9JwMbMnMzM+6je43hvY+5leu4zMvP2+vYI8HPg+cCWzHwkM38K3AX8\nbm9j7r/5XhBHAD/tuL87IgZ2t1tmPpiZExExClwFrAKGMnPqWOUJ4Mi+BZxBRPwJsC0zb+wYHvjc\ntSdQ/eLweuBtwOeozuof9OwPUu1e+i6wDriYAf+eZ+bVVEU2pZR3+r/Zvr+P6bkz84cAEXEi8Hbg\nwwxg7m7M94Jo3eU8IuJo4D+Az2bmFUDnPuRRYGdfgs3ubKqTHr8CPAf4DPDEjscHNTfAduDGzHw0\nM5Pqt8HOf9iDmv1dVLmfSbXG9mmqNZQpg5q7U+lne/q/2YF8HxFxOtUW82mZuY2W5J5uvhdEqy7n\nERFHARuB8zNzfT18W72fHKp1ic39yDabzHxRZi6p98neDrwJ2DDouWtfBV4eEUMR8WTgN4B/b0H2\nHTz2G+tPgENowc/KNKW8W4BlETEcEcdQ/VJ3f78ClkTEmVRbDksz8556+Bbg5Ig4PCKOBH6HauF9\noA3s7pQeadvlPN4HjAEXRMTUWsS5wMURcShwJ9WupzY4D1g36Lkz8/qIeBHVP/BhYAVwL4Of/cPA\n+ojYTLXl8D7gmwx+7k57/Yxk5u76Pd3MY38fAyMiFlDtzrsP+GJEAGzKzNURcTFVyQ0D78/Mn/cv\naXe81IYkqWi+72KSJM3AgpAkFVkQkqQiC0KSVGRBSJKKLAhJUpEFIUkq+n89sBIIwXuUgwAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b84c048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['frequency'].plot(kind='hist', bins=50)\n",
    "print(data['frequency'].describe())\n",
    "print(sum(data['frequency'] == 0)/float(len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.BetaGeoFitter: fitted with 4339 subjects, a: 0.00, alpha: 69.01, b: 1.18, r: 0.83>\n"
     ]
    }
   ],
   "source": [
    "from lifetimes import BetaGeoFitter\n",
    "\n",
    "# similar API to scikit-learn and lifelines.\n",
    "bgf = BetaGeoFitter(penalizer_coef=0.0)\n",
    "bgf.fit(data['frequency'], data['recency'], data['T'])\n",
    "print(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11c0c6be0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/KO6+HmHU4ELCt+mPFvd/hUH/nXsRgrh+8bu/KI53A+C5FrpVPxD4cFrUzd2vsNCw9K/M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\n4zhLhwscx3Ecx3GWDhc4juM4juMsHf8f0PZQAPwlxI4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c0b1550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_frequency_recency_matrix\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "plot_frequency_recency_matrix(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11bf9fe10>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Tbjkx41qz29PSTDKdFEIIsUdpKc20uAyH8cCXaIie3+7HRpOdVnW/03GRmTzp\nZmqI0hVCCCEWgaURM1GUJn2upjWbJDKTt6r7rjM7GqAH0wqA3T5JKkoTgYUQQuw4Dfny3TgxM3Si\nJevM9ksa1dTMjFIxQ3XfB2M2pZlUMyOEEELsGI0TM0IIIYSYjbrswaKxlGJmesrJPdeLa2by4eQ0\nU96Ja2Z8a7bflk+TEEKIPUVDMglzFTNmdirw3BDCmWZ2J+C1wAi4DHhyCGFoZs8CHgj0gaeGED4y\nzzVNYjisSTMNUjFTzZ3pOgftLKmZyWaomRFCCCHE0WFuYsbMfh14DHBD+dCLgN8JIVxkZq8EHmJm\nVwBnAKcCtwXeCtxtXmuqIxqaFw3Qi8VMNqzu+5qZPO1makvACCGEWAAa8oV7nu/iC8DD3f27Ah8o\nt98F3B+4J3BhCGEUQvhPIDezm89xTVsyGg43bgwG0S0frG/cOvlw49Zut6JbK6tuWau6CSGEEOLo\nM7fITAjhrWZ2onuoFUIYhz2uA74FOA74httn/PiV81oXwLCf2BkMfGt2tT3qxd1M3kW7067Okeex\nJvQu2vJpEkIIsWdpyBftnSwA9iWv+4GrgWvL7fTxqdz70vM57qQ7A/CgfjiKS5ydB/rtUzrJs99R\nsz0fDpx/xtxfYxHQdSjQdSjQdSjQdSjQdWg2OylmPmFmZ4YQLgIeALwfuBx4npm9ALgNkIUQrtrq\nRBff5WygEDJvz612Pz9npr2viorkx8U1Lje5deV1cMIdvnVj+1anfm+03+CeP7qx/ZH2vTa2P3hp\nrGz//dNf29i++n++ubF96PobN7b763HUZ7tD8w6cfwb3OPsDW+/YcHQdCnQdCnQdCnQdCvbqddgL\nAqspTSo7KWZ+DXiVmXWBzwJvCSEMzOyDwCUU9TtP3sH1bOCNJkdRZ1NcANx2aaa8UwWa8jy+jOkQ\nvTF1Pk0gryYhhBC7gLyZtiaE8CXgtHL78xSdS+k+5wLnznMdh0PczRQLjJZz0fYO2p08TjP5biZN\nAxZCCCHmy9IMzUuLfj2jKDLjCoCTaEnLFwA7MZPnsWDxkZlZfJogFj3yaRJCCLEjyJtpcZl1AvBw\nxshMng7Nc3Nn5KAthBBCzJelFDMpkYDxUZpNkRlnNJlV9TSdThqZcRYGUZv2ZGsDkL2BEEKInael\nmplmEqWZksgMPZdmajkxk1zFOM2kyIwQQog9SkM+o5ohyYQQQgixtCgyw7TW7ClpptZkB22IXbRl\nOimEEGLPojRTM4nrZ5I0k5s7k+OETTyDL3LR9m3a8mcSQgghjj5LKWamtWlHUZokMjPykZlhtd3N\n4/N5F+26mpnNURoNzRNCCLHnAUvKAAAgAElEQVTDNORL9lKKmZRRTZrJbwMQiRlXDJyIGd/NVGc6\nmeKf0zRgIYQQO0JDyh8kZqaQ1szgREY2dCmndhqZmdzNFG03RA0LIYQQu43ETELUmp1EZkY9F5kZ\nuMhMKmY6lZhpb8PaQNOAhRBC7AgNKQBuxrsQQgghxNKiyAwwjPyY6luzR66bKfM+Te14fK9PM2Xb\n8GkSQgghdoSGDM2TmEkYTikA9t1N7cHaxnZnJRY9HdfN5NNM03ya/HOyNhBCCCFmR2JmCpsiM65m\nJhs4O4Ms3s+7aGf55G4m2RwIIYTYdRpSM7OUYiZ1zfb3p7Vm+5bpKM2UiBlvPOnbtNXBJIQQYk/R\nkM+lpRQzs+I7mwCGvSoa0x44O4M0MhPNmXGdTTVRGiGEEEJsn6URM1E0Jq9XoqPBlNZsH5lxDtq5\nc9AG6HbcSzmfJh+ZSa0NYnGjoXlCCCF2gIZ8sW7GuxBCCCHE0rI0kZlZGU5pzY7u+zRTEpnxxpPe\ndDKeBixrAyGEELuMamaaQ53x5LQ0U+TT1OpF+3XdVc1r2rRT6oqD08c1EVgIIcRRQ91MzSQamjeo\nnzPT8mJmFIsZbzzpu5myGdy0hRBCCHF4SMxMYVM3k08z+QJg56ANsfFkZDrZqm/TVneTEEKIHach\nnz2NFjND18GUdWaLhEybMzN0aaaRj8wM6yMztaaTU/6ANA1YCCGEmJ1Gi5lZSYfobTw+xc6Agbc2\niCMzXefVFE8Drrc2UNpJCCHEjqMCYCGEEEIsNCoAbiZp0a8nSkE5n6Y0MuNdtDt5dYkj08l2GyGE\nEEIcOUspZtJW7DpZkQobXwA86lezZbJNNTNOzLiamWga8KY0U109jebMCCGEmBNKMzWfTTUzdZGZ\nfhKZ6VYCxAVm4shMUgCc2huMSQuFNURPCCGEiJGYSfBzZqa2Zg/8zJmkNTurojZdXwAcpZlikTJr\na7Zv6dYAPSGEEEeEWrObzygdmuciM3UO2hC7aPvIjG/Tnta9VDcNWAghhBCbkZih3s5g836uZmZa\nZMZ5NXVq0kztpABYrdlCCCF2mlFDvjxLzAghhBDLilqzm8nQ1ckMpxQAD9er1JL3aQLotqpITWw6\nOaVmpjXZUTsdrqeJwEIIIUSMxMwUNnczVUoi6irq1aeZ6nyaNk8AboY6FkIIsUAoMrN8DPtOzNQ4\naENsPFnn05RGZry4Uf2MEEIIMTsSMwnep2mU5HR8ZMabTjKoFzPdKDJTiZR2KmbafqDeNENKzZkR\nQghxdFAB8BKQTgCOhub5zqZeLGbabiJwNA3Yp5ny7XUzReKmFFetVkszZ4QQQhw+SjM1hzrX7BQv\nbnzKCWdtAJA7ryY/c6bj+rR9/QzEE4HrpgELIYQQYjMSM0IIIcSy0pAvzxIzU9g8AbimmykpAM7c\nEL1OpzqmzqcJ4oLgqGamIX9oQgghxLyQmEmYNg04mjMzpWbGu2h3a3yavIM2xDUz6mYSQgixIzRk\nLIjEzBSmumb7KE1SM+NdtOt8mtrtWLB4e4O6AXoQt3BrgJ4QQogjQd1MC8ymgt98tl9mXQFwGpnx\nXk3eQbtTMw0Y6tNMQgghhJjOUoqZWZnWmh2lmfrx7Jd2f21ju9PyaaZqHz9AD+IaGg3QE0IIsSOo\nNbuZTGvTjlJLkbBJWrPd/bzlZ85MtjYAyPKaAuAkShM/N6oe82vTzBkhhBBLxJZixsy6IYT1rfZb\nNqZFZnCRmRxXDDxFzESRmXYzlLIQQoi9zaghkZlZ3sXlZvanZna3ua9GCCGEEOIwmSXN9F3AjwN/\naGa3AP4a+JsQwtfmurI9wKY5MwPfzeTSTJsKgF1qaeDqZ9p+5kzazeRrZuqnAWvujBBCiKNGQz5T\nthQzIYQbgdcBrzOzhwEvAc41s/cCTwshXD7nNc4dP1umPW2/2tbsNM3kama8T5MTM91ufOmjbqYp\nrdlCCCHE0WI30kxmlgEvB04G1oDHeS1hZg8AnlXe/Tjw5BDC1GLQWWpm7gQ8BngkcAXwG8DfA/cF\n3gV855RjTwWeG0I408xOAc4H/r18+hUhhDea2bOABwJ94KkhhI9staadYjhMXbMnt2ZHDtrAaL2K\nxrS9T5OPzCRzZvwQvbgYOInMZJu7nrKspZkzQgghFoWHAqshhNPN7DTghcBDAMxsP/B84MwQwlVm\n9uvAzYArp51wljTTe4DXAmeFEK5wj7/TzM6qO6hcwGOAG8qHTgFeFEJ4odvnFOAM4FTgtsBbgbnU\n5gxdl1LWqQ+rTZsA7Jk1MhOLGW86WZ9mqhugJ4QQQhxVducz5p7AuwFCCB82sx90z90d+BTwQjO7\nA/DqEMJUIQOziRkDfjSEcIWZ3Qx4MPCXIYRRCOFXphz3BeDhFCkqgLsCZmYPoYjOPLV8QxeW4aP/\nNLPczG4+y8J3g9GgrjU7CYu4mpm2q5npdt3MmU58iJ87E1sbpK3ZW//hpQJIrdpCCCH2EMcB17j7\nAzPLQwh9iijMfYC7ANcDHzSzS0IIn592wlmSZa+kKAAec5/ysamEEN4K+MrYjwD/L4Rwb+CLFPmw\n9A1dB3zLDGvaEUa9UXQbDibfRoNBfOv1Nm5Zf33j1skGG7e8TXzLs41bu13dsqwV3TxjodPKsugm\nhBBCzEQrm89tOtcC+939rBQyAN8A/jWE8LUQwvXAxRTCZiqzRGbuFkL4PoAQwlXAY8zskzMcl3Je\nCOHq8TbwUuAfid/QfuDq9MCUe196PseddGcAHtQP21jK7nCK375z8uT9jnF3/PZttjzvRW85/QhW\n1RwOnH/Gbi9hT6DrUKDrUKDrUKDrMJld8mY6AJwNvKmsmfmUe+5jwEllJuhq4DTgVVudcBYxk5nZ\nrUMI/w1Qtmdvp9z0AjP7pbLA937lgg8AzzOzF1B8amelYJrKxXc5GyiEzNtzO+yFpDUzLXe/va9S\nlJ39cW/T6gkrG9v7b3WTje3jb3+LaL+bnlTVRI9OqkqAvniz0za2/+2r8TGf+fcqHfXlL/3vxvY1\nV10b7XfjdTdsbPfX1rnoLadz5k9cwsAP8UsLl5cgzXTg/DO4x9kf2O1l7Dq6DgW6DgW6DgV79Tos\nscA6DzjLzD4EtIBzzOxXgctDCG8zs98CLij3fVMI4bKtTjiLmPl94BNm9s/l/VOBpxz+2vkF4GVm\ntg58DXhCCOFaM/sgcAlFyuvJ2zjvjlE7ZyYpAPYFwa2Ba81uedPJWGD4mpl2e3L9DMRzZ8a1MSoS\nFkIIsS12oTU7hDAEnpg8/Dn3/N8Bf3c455xlzswbzOwi4HSKGphfGkdpZjj2SxQhIkIIH6eoUk73\nORc4d9YF7xVGw8nCBmIX7cw5aHdabjsVM26IXtSmPcWbSQghhBCzzZm5KfAw4ASKcNBdzIwQwnPm\nvbjdwBtNpm3aUTRmUB+Z8caTea8SMPnI+TS143N3XWQmm+LTNKnTqZVlUXGwZs4IIYSYhRHNiOzP\nkmZ6M0XH0WVA84svZmRqZMaLG9emnQ8rYdPNYwGU51Wvto/MbBqat42Ukj9mGepnhBBCzEZTjCZn\nETO3CiHUDsdbJoZRzYybAJxGZlyaqeUjMzXTgAG6vgi5ZoAexGmmsdCZNiU4XasQQgjRNGaRZJ8w\ns++f+0qEEEIIsbPszpyZo84skZmTKATN14FDFHUzoxDCHea6sj1OXWcTTEkzeQftLI7mdNxE4Lym\nfgbYNDhvTBSNGQ4m7iOEEEI0kVnEzMPmvoo9ii8GnsamNJMznhz1J3c2dVf70TG5yybluU8z1Xcz\n+QJgIYQQ4nDZpaF5R50tPwVLc8l7AE+gcK08IzGcXBpGg9HGbTisbqP01h9s3Oj1N27twdrGzVsb\ndLIB3ZyNm7c2yJJbq9XauI1nzmTuMc2cEUIIsWzM0pr9RxTTee8KPJdiUt/JIYRfm/fidoooApPP\nJgbibqa4wNYbT9ZFZvJWHJnpuN9E3QA9gHbuO50mR2bSVJRatYUQQkximbqZfoTCVujj5cTes4BP\nAo0RM7MydKKlzkG7eM6lmWoG6HXdAD2AlU51vroBehC3WftupkjQDOprZtSmLYQQYoOGRPNnETPj\nT9nxJ98K2/NmaiyDXjo0z4uZKgKTOWuDzZGZSlh0p0RmMldPM6udgRc6atMWQgjRNGYRM28C3gic\nYGZPBR4LvGGuqxJCCCHE3FmaNFMI4blm9iPAFcDtgGeEEN4x95XtEt7CoNWvT8MMp7Rmx5GZyQP0\nOsO16JiuG6LXcQU0aZrJD9HzNTOTbA7cYmvfhxBCCLHozFIA/G3AfUMI/8/Mbg8828w+GkL4+vyX\nt7eoa9WeJma8TxN+GvAwrpnxE4E7vmYmT9JM3repFDBZWjMjhBBCzMAyeTO9nsqK+6vAB4HXAT88\nr0UtAn5ono/SQNLp5IRNy3U2tYe96Jhuu9rPD9BLh+b5GprIaNIXBjekoEsIIcR8WZo0E3BCCOHP\nAEIIa8CrzOwX5rusvc80o8koMuPSTNT4NAF0nJjput9Kt1tfADwWOqngSZGjthBCiCYzi5g5aGYP\nCCG8C8DM7g/cMN9l7U2GNTU0aYdQXWTGz5xp9w9Fx3Q7VToqmjmT10dmsjIyk2XZxMnAG9S0aqcR\nHLVqCyHEktGQSP4sYuaJwN+Y2eso2rO/DDxmrquaM8Ok9iXrHP4vM00tRc/5yIwXEutVNKbdjyMz\neVaJma5r007FjC8I9pGZ1Dm7DrVpCyGEaBqzdDNdCpxkZt8K9EII185/WUIIIYSYN6OtXY0Wglm6\nmb4DeDVwInAvM/sH4GdDCF+a79J2n03dS/tq9ptSADxcryIuPs3USiIz3Vb1XLfjBuh144iLTzON\nt9vtbOJk4Oq+HLWFEEJspilGk7Okmf4MeD6FL9PXgb8F/hq49xzXtVAMpxUA11obxHNmci9m2j7N\nFP+h+TST72aa5NkkhBBCLAOzfOrdLIRwIUAIYRRCeBVw3HyXtTcZ9UbVzTlob3LNrnHQHvX6G7dW\nfz26dUbulg+rW6cV3SJH7ahmprqlyFFbCCHEJEatbC63nWbWbqbbUHozmdk9gbXphyw3vjh4lmnA\nEA/R60Zt2p14v3zrNFOWiBafWJrWpi0TSiGEEIvILGLmV4G3A3c0s0uBE4BHzHVVC0CdgzbEXULD\nvt/PyYp+PDQvH1T6sJNNHqAHkDsTynHKKe+0p6aZ6hy10/3U3SSEEMvF0kwADiH8q5ndDbgz0AY+\nR+GcLUqmTgD2wsY5aG+KzLghet3ct2nHr+UjM1kpYLK8PbUA2KNiYCGEEE2jVsyY2c0pojL/C7w4\nhPBpM8uAnwfOBW65IysUQgghxFxYBjuD1wPXATcDumZ2HkUn037gV3ZgbbtC1I6dby/8FrVm931k\npkotjdbjsqPMtWp3ui7NNCUyM97O8yyyOUgLfaNIjYIxQgghSpahNfuOIYQ7mtl+4BLgScBLgReF\nENanHNdYvJ2BFz3pnJnaAuC+r5np+0PInb1Bx7Vpr3TiOhY/d8YXALfbVc2Mr58BtWoLIYRoNtPE\nzLUAIYTrzOwE4MdDCJfszLL2BqkXU7vG9iA1mqwzofQ1M2kBsB+i1225KE0en7tTUwCcTXDTHlPn\nqJ0ltTW+jlmdTUII0XyWoQDYf4J9fdmEzJEQdzMNJm+vx8EtP0Qvb7kC4HYSmXFD88adTXkniyYD\nb04zzRaZkW+TEEKIRWSamNlvZveiGKx3bLm98SkZQrh43ovby/iozaZupkFNZKZmGjAkNTPDStj4\nmTMAHderXVczsznN5DudJrdpCyGEWD6WoQD4y8Bzyu2vuG0oojb3ndeiFp1hTWv2KBqgF9fM+Fbt\nzqBezPhWbS9mclcpvCkyU9O2vSlio1ZtIYRYKhqfZgoh3GcnFyKEEEIIsR1mmQAsSqK2beegPc01\ne9CbXD+TpplavSoa03YD9Pw0YIhbtbvdbONnu+0Ke/MpE4CFEEKIkmVIM4mjwEzWBgAuzeTbtLv7\n4nRUN/eO2i7N5OpkfJs2xF1LXtik6ag636Z0P3U3CSGE2EtIzGyTKEqTPueUQDxAz3UzJTUzPlKT\n+chMK47gdDvV+Tplq3in09po0waiNm2IBYxv055WIaPOJiGEaD6Nr5kZY2Y/BNwTeBmF4eQPAI8J\nIbx7zmvbMYZOmGQ1s2SmHp982A9rupkiYbMeixQfmWnXzJwB6Larc3TL1uxupxUZULYTMVM3g2ZT\n+kndTUIIsVQsU5rpJcAzgZ8AbgROAf4eaIyYmSd104CHiXCIIjO9Ks3kZ84AdHPvqN0uf7YSA8pE\nzEQCpt6QUiaUQgghFpFZxEwWQrjQzF4PvDWE8F9mpvSUI0051c6ZqbM2AEbO3qBVM3MGYjHT7VQ/\nI8+mxNApmzJQbztoOrAQQjSDpUkzATea2a9RzJX5RTP7ZQoDyqXGD81rJ8+N6ubMRF1OSc3MWiVg\nMtfZ5GfOAKy47qaVTvVz3NkEsbCBOO3kB+qlaaY6q4OBSmaEEELsYWZJlv0UcCyFN9M3gW8HHjXX\nVQkhhBBi7oxarbncdprayIyZPZOiRuYTIYSN6b8hhN/YiYXtBTZ1LOWH/wsazeKgTTJ3xhcDD+IC\n4LxdRXTG2aROHkdjNhUA10RjsuQPrq5KJo3gqLtJCCHEXmJamun2wEHgf3doLXueKLXkup5Sd+2o\n6LeumykRM0NfM1Mzcwag26n2W+kMgTYrneFGmzYQtWkDtSaUm9JM8m0SQoilYjRqeM1MCOEcADO7\nAHjNjq2oYcRGk17MxNGNKFLTr6I07VTMZNVznXKAXicfbbRpA1GbNsQFwHHNTNrNVCN01NkkhBCN\nZDRTtcneZ5YC4H1mdtsQwn/NfTUNIbU32Hh8ONnaAGDo0kyjdVcM3I/TTB03d2YlH2787LhoTCeJ\nzNQN1Ju1sylLRE/ddGB1NgkhhNgNZhEzNwe+ZGb/Q5F2agGjEMId5rqyPU6dT9Om/QaT7Qw2i5kq\nfTRarzqYNomZkRuoVzpqd9sDVsZ92kCnU9/NNM01u87qIJUomg4shBDNYJlas3907qtYcNJCYT8R\nOEot1cyfgTjNFM2c6cVpps7A+TaVxcDddp+u+02mYsZHZrxvk085QVwQPFT9jBBCiAVhy2RZCOEK\n4B7AE4ArgTPKx4QQQgixwIxozeW208zizfRHwG2AuwLPBc4xs5NDCL8278U1gVmmAQMM1l2aKbI2\niNNM7WH1XDfrb/xccQaU3W78h+QjM347rZnZ5NVU97gKgoUQohEsU5rpRyj8mD4eQrjWzM4CPglI\nzBwmddOAAUYuleOnAbd68QTgjutu6q5UYmbc2QQT0kzet6mmswmm+DbNqF1UDCyEEGI3mEXMjD+B\nx59OK+4xMQFfQxNZG9QM0Evv+5kzpJEZL2b2FVGabtZjxYmZ7hQx44uBs2S4Xt0MmjSC47ubhqgY\nWAghFpVlisy8CXgjcIKZPRV4DPCGua5qwUiH5qVeTRv71QzQK84xeTqwb9MGaHvfprJNu9Nan+im\nvXG/OznNlE4K9pEa7x2lpJIQQoi9zJZiJoTwXDP7EeAK4HbAs0IIb9/qODPrUAzbO5EimvN7wGeA\n11JEeS4DnhxCGJrZs4AHAn3gqSGEj2zr3RwFhi6qknWOXLEOa2bODHpTIjPe2sAN0IPEUbts0+6M\nYjGz0okOiU0o/cyZTWmmbMttgJZPIal+RgghFpbGTwBO+Cpw/viOmd07hHDxFsc8GvhGCOExZvat\nwCeAS4HfCSFcZGavBB5iZlcAZwCnArcF3grc7TDfx45TZ22QPucZTY3MuHbuaOZMHJnJXKv2uE27\nMzgUuWl3k9+qTzNNi8xktfNokj/2GfRLmppSDY0QQuw9libNZGZ/R1EA/BX38Ai47xaHvhl4i7vf\np+iI+kB5/13ADwMBuDCEMAL+08xyM7t5COHK2d6CEEIIIZaZ1lbfmM3ss8BJIYRt5RPMbD/wNuBV\nwAtCCN9WPn5f4GeBz1FEcF5RPn4x8LMhhMvrznntZZ8fHXfSnbezHCGEEGKvsOthkcsu/9pcwuYn\n3elWO/reZkkz/QtwJ4oIymFhZrcFzgNeHkJ4g5k9zz29H7gauLbcTh+v5eK7nA3Ag/qBt+d2uMua\nmWk1My33XHtfUkjr7neOzSdu7zs+9kC4yS2qS3CTW59QbZ/4bfG5b3+nje0bb/M9fOv33YNvfOoA\nX179zo3H/+PqE6Jj/uO/q/V85csHN7a/ceX10X7X/m91/+D11X7rh+L28MF6VcczdC3lcYFzYqQ5\n5zTTgfPP4B5nf2DrHRuOrkOBrkOBrkPBXr0OB84/Y7eX0BhmETPvAz5tZl+lSBXN5M1kZrcELgR+\nMYTwvvLhT5jZmSGEi4AHAO8HLgeeZ2YvoBjOl4UQrtrWu9klUjuDkWuTHta0K0/tZvICwdXPAOSu\nVXvcpt3uH6LbqgTG2IByTNcV+vrOpk3dTL5t29XJZEn9y3asDjSDRggh9h5LUzMDPJ2iPuZwLQye\nDhwPPMPMnlE+9hTgJWbWBT4LvCWEMDCzDwKXUNgrPPkwX2dhiKcBx4LDixkf+fDTgCE2oRy3abd7\na5Gb9tiAcow3oazrbIK4uylzHk51k4E3PafOJiGEWCiWqZvpKuCDZYHuzIQQnkIhXlI2xdVCCOcC\n5x7O+ReFWQbopc/VdTYB0RC9cWdT1jtEd+gNKGNR0XG/5brOpuK5ySaUaTdT3XTgumF6oIF6Qggh\n5scsYubzwIfN7D3AxidpCOE5c1vVEjBM00w104GH62lkxlkdlDNnWv11OoMqYjN20x7jfZtWVirB\n4VNOAFk+eeqvj9JA/XRgJY+EEGKxGC5Rmuk/yxvsgcprIYQQQgjPLBOAn21mN6cYapcDl4QQvj73\nlS0w0UA9/3iNg3ZxzGDydpJmihy114vUUmv9ELn3bOrWR2Y6rgvLp5wAcpeP8lGaLEkz+YJgXww8\n62RgFQMLIcTeYGkKgEsrg9cAH6Yo0P0zM/u5WSwNxJRpwIOkdblmOnBqSBmlmcoC4FZvjXa/SjOt\nrMZTg7uuu6mbV7/ybjetmfGGlPUFwNMKgoUQQoidZpY00+8D9wwh/AeAmd0B+HtAYuYwiVyzBzPW\nzCSRmej+uBi4tx5FZnxnE8CK921yXged1F27M9mQcpO7do3VQWvo6mySaI7ctYUQYu+xTN1MnbGQ\nAQghfNHMluKr+TCZH1M3RG+Ta/Y2DCpru5nSyIxLM42jNKP19YkGlGNWXEHwSmdlY7vbjdeZO3Hj\nBUw7LQBueTHj/xQOvzVbHk5CCLF7LE2aicIv6anAX5T3H8fhz5xpHL7lujVFvPj9/AC9za3Zw4nb\nqZiJIjPjlNP6+kQDyjG+u6kb1c8kkZm8JjKT1Nb4tu2BW09t/QxoBo0QQoi5MYuY+TngpcBvU3Qz\n/RPw+HkuatGJJgLnk4VOWgDsxc2gN0XM+IF65QC90fraRjEwQKefiJmOj8y4+plkzkzdQL1NkRkv\nWqLtyfNnoH4GjVJOQgixeyxTmunkEMJP+gfM7OEUdTNCCCGEELtKrZgxs58EVoDnmNkzk2OejsTM\nYRNFbFbj5+pMGn39DMRpplG/v/Gz5SYD50lkZmWles77Nq0k3Ux+iF6e1xcA+/vpdOCNx9NamIl7\nCSGE2E2WoWZmP3CP8ud93ON9ipSTOALSbqZZW7OjTqe19Y2fbZdmaidips63qdvpRPt1O5PTTKnt\ngU871Xs4ba9GRjNohBBi52h8mimE8Grg1WZ2P+d6jZkdF0K4dkdW1wDqBuil+LkzU2tmfGSm7Gwa\n9XqRAWXWW4uO8d1NK7mvn4nXEA3U6/hupiQyUzNQr26YHsw+UE8IIYQ4XGapmTnGzJ4L/C7wr8DN\nzexpIYTXznVlDcQLm7SbqW468KY004QZNMNef6IB5Zju4GC1nU0uBobEt+kIIzOb0k8ypBRCiD1H\nU/7HnUXMPJOiHfv/Ah8Bngx8AHjt/Ja1fIwGk2tm0g/3wXolRgZlmmmwth5NBs568ZyZ3E8H7lbd\nUCt5LKi6LuJS19kE9TUz0eODJDKzDUNKpZyEEELMwixihhDCv5nZucDfhBCuN7POVscsM1FqqW7Q\n3qYIRCUY6tq0i3MP3H6DjZ+RzcF6HJmJfJtWnJjpxOkeXxDccWKm043/TOratn1kJksKgLfj4SSE\nEGK+NL5mxvF1M3sp8IPAo83shVQu2kIIIYRYUJahm2nMI4GHAX8SQrjBzL4IPGu+y2omUWv2vuQ5\nXydT06YNSc1MOUBvuN6LbA5aSQFw3nM1My2XcmonkRkXb4s7m+o9nOqKgWc1o5SHkxBCiCNlFjHz\nsPLn3c3s7sB1wMOBv57bqvYo3qvJ+zSNEg+nVt1zef0xw87kAuB0UrAvCB5bCQx6/Y02bYDRWpxm\niqwOhl7M9KL9up1q+M1Kd3IxMMTdTfXFwLFBZp0h5XbqZ0A1NEIIcTRYpjSTnzHTAe4FXMwSipmd\noq5NG5Li4DJKM+oPJrtpl3gx0+27KE07Fhyr3ckD9XwxMMQ1NFH9jBu0l4qPuhk0myI4qqERQghx\nmGwpZkII5/j7ZnYC8Ma5rajB+MLgVuK07Yt+69q0i3M4oVN2Ng3W+wwnuGlvvJafDjyoIjPdTuKu\nXTMduNOdkmZyUZrIaTuPozl1hpTjIuaNc8jDSQghdozdqJkxswx4OXAysAY8LoRw+YR93gH8Ywjh\nlVudc6ZupoTrgRO3cZzYBlNrZsrtYRKZ2SRmXHdT3rtxY3tlX1xbEw/Uqwpoup00MjN5Bk07atlO\nWrNrZtD4lBOobVsIIZaAhwKrIYTTzew04IXAQ5J9fg84YdYTbilmzOz9VJ8xLeAOFGpJHEV8q3Y0\nc2bKcL1xlGbYH0Zu2r5+BoitDlxxsJ8MDLDq0k5dV8Pj62cA8nzyDJpsVj+nweSUkxBCiJ1luDvf\nBe8JvBsghPBhM/tB/wtziAkAACAASURBVKSZ/QTFPL93zXrCWSIz57rtEXBVCOEzs76AEEIIIfYm\nu9SafRxwjbs/MLM8hNA3s5OARwE/QTG0dyamihkzOx74dAjhqvL+GcCVh71ssYm0m8m3ate1aUN9\nmmkwwbNp4/76ZKsDb3MA9VYHqbv2yqqvp3HFwPnkYXpQP1BvmodT5gZty/ZACCEaw7UUJtZjshDC\n+APoscC3A/9EUdKybmZfCiG8e9oJa8WMmf0A8E7gHMpwEPDDwBvM7AEhhE9u6y0sGbNMA4ZE3Ky6\nxxMxM8lRe9gfbHQ2QWxGCYCfDuzbtHuJmFmp9ludImbqZtDUzZ+BuCB40Kv3cDqStu1Wq6X6GSGE\nOAx2qTX7AHA28KayZuZT4ydCCL8+3i6dB762lZCB6ZGZFwCPDCFc5F7kt83sYuBFwP0Pd/XLTt3M\nmZSom2kwrH3O18xM8mzaOIdz1PbFwO1+UgDsCoLrioEhNqTs1hhSborMtPxAvWnD9VRDI4QQDec8\n4Cwz+xBFLe45ZvarwOUhhLdt54TTxMzxXsiMCSFcULpoixq8aGlNicbUHl/Tpg1TupmiyEycZhq6\nyEy+NrmzCaA7qsSMLwZe7cZr6Lj3VNfZtMlpO588XC/rx+KlzsMpS7xd69q21eUkhBCzsxv/TYYQ\nhsATk4c/N2G/c2c95zQx0zGzrHzRDcre7+6sL9BU6qYBz3x8MmfGz51pr1SPp91Mk4TOcDCK5s8M\n1+M008hHanq+fiaOzHQGrp4m851NsZCoG6gXRWamOG1Psz040knBQgghZme4BN5MH6DwYEp9mH4H\n+OjcViQSR+128tzkmpkoMpMMovORGW914IuBATreXbvr6mfy+HyrTsysrHh3bR+ZSZ22q/u9qbYH\nmhQshBDi8JgmZn4LeKeZ/TRwKXAIOAX4H+DBO7A2IYQQQsyRxnszhRCuM7N7U3gz/QDFAJs/DSF8\ncKcWt0zUOWpP62Yab4+Go8RNO4521E0H9sXAELtrr6y6+pl8iru2SzN5Q8o8rx+aV1c/A3ENzeHa\nHrSyrLZ+BlRDI4QQTWXqnJkQwoii1/ufdmY5zWY7bdreTRvi7qa6mplBKmbWJ/s2ZYm7du7TTKN6\nd+3VblXUs+LETF39THq/rn4Gjr7tgRBCiHqa8h1vO95M4iiwaWjelFZtT9yaXVMzk3YIeZNHVwzc\nTiIz2bpz1HYD9TaJmWgGTSU+VlZ8YXC9mGlH5pTpcL2+2663PYieG06urdFgPSGEmM4uTQA+6kjM\n7EF8BGdaN9N4ezQYTRQ5Y3ykJioGTgwps5qBeiurqbt2df4VV9jr5890pokZd0w7j6NIdW3b6aRg\nn3YaR3eyrLVpYrJHbdtCCNFMJGbmzKwzZ+pSUMNN0YW2e2608TOOzCQzWdzcmSjllKSZInftvovS\ntJLhetEMmqpLP045xWImsj2oSTlBfdv20ZgULIQQImaXjCaPOhIzC0ZdAfAkm4MxUWRmbUpkxg/U\n8ymnYSx6VvNKEK12J9sedFdikVJne9De5K49uW178zwaJxLLKEsry2b2c1KURgghmoPEzFFgmNS/\nbGeInsdHc0Z5MgG449NMw42fg577EE9rZmp8m4aJ7YGvoYkMKfuxh9NKPnkGTTR/phsLiVrbg2Qe\njU87TZ0UjBBCiCOlKa3ZqTGOEEIIIcRCocjMAuNbs30KxUdpgNq27WGSZoqmA69V0ZhOGpnpTJ5B\ns+KiRr4YGGBl1dXM5JOjNFA/j8Y7bcPktu1WqwU1XU7FMVv7OYHSTkKI5aEp/91JzOwSqTdT9FE9\npU27rpspejwpGo4ETE0xMNQP1Gv3YjHT3Td5Bk3d/BmAjquZ6azUi5nI9mCtOndaKNwa+OLgqmZm\nUpfTmGmdTkIIsYwsgzeT2CW80GmlhpSdyb5NsWdTGpmZPIMmrZkZHvIFwE7MrCdixs2gWW27+pmO\nr5+JxYf3cKqrn4FYtHhh0+/FLdxtV08zFm+trKUuJyGEWEIkZnaQWdu0Zz5fXTdTMpvGC5g4SlPv\nru1TTu31G6P9ur3qvp9BE8+f6UTHrHRb7pjqz863bEMsbnr55JQTxGaa4/RR8bPenLKu0ymNZKnT\nSQixLDTlvziJmT1OOinYdzeNO5uGg1Fsc5B0/oxqojabbQ9cpGaah1PNDJp9Uct2NzpmddV7ONXP\no4nbtuvn0XjBkZXbWas11c9JCCFEM5GYWWDqJgCnU4MHvbrITFwzE7dt+8hMImZc2mll4KI0rn7m\nmG5qTultD5ywmXG4XjuxPfCRmuFgnGbKpvo51RUHpxEczaMRQiwLTWnNlpgRQgghlpSm9EVIzMwB\nP0Rv1gF6vuh3WmdTZHtQNQ9F0Zi0a8enlurqZwAGUc2MSzmtxXYGkYeTSzmtdl2XU35MdMxqt6qh\nWV2t3lOaZuquVH+Sh6YUCvd7PgU1KH9mE7ucxtR1OqnLSQghFhuJmT1O2sI9ybdpOBwyGvqC1kTM\n1JhQbpoUvO7bticXA0Myg8a1bXdX3PyZdiyUYtsDVzOT2B74tJPvZsry+jRTv1cVAE/qchoza6fT\nLPNolHISQjSBpvxXJjHTEOKamfhDfJKfE0yIzNRYHWwypFyr6mTy3uT6mdU8bvs+xs2g8W3bm+fR\nOH8nJ2zWEzHTmzBcr523J3Y5Vfc3+zlB3OUEitQIIcSiITGzS6RdSrO2ak/ybRr1RuA6oTe1ZvsC\n4N4Ud20nbnzKyc+fgXgGTeaKgTuD6vHVTuK07dJO+1yR777VZB7NaiVa6oqBi/ubZ9Bk7Wyqn9Oo\npjj4SKM0oEiNEGIxGWlonthLTJoMPKZuoN5Ud23X6TRam2J74GbQdNdvqLa7sZipa9teTW0PupM7\nnTor8Z9qz611nFpqt9sMpjltR4Jjxnk0itIIIRpMU/6Lm5uYMbMO8BrgRGAF+D3gy8D5wL+Xu70i\nhPBGM3sW8ECgDzw1hPCRea1rEagtBoaoIHi837A/iiYD+/qZ4v7kgXrT3LUHhybXzwCMXKSmdaiK\nzNSlnABW2/s3tvd1V6vHp0wKXnG2B4eS4XrtCcXBeac9sTB4Y90usjKM2rSTtByTqYvSgOpphBBi\nN5lnZObRwDdCCI8xs28FPgE8B3hRCOGF453M7BTgDOBU4LbAW4G7zXFdQgghhEAFwLPwZuAt7n4f\nuCtgZvYQiujMU4F7AheGEEbAf5pZbmY3DyFcOce17RjbadOeej7fml1zvrRmpm46cOquXZdmGiRp\nptxFarIZ6mcAVjrVMfvy6nVWk4iLTzv5yMzmScGbO52yvJ0M00stEFzNi6ufGcWXIYrAKOUkhBB7\nn9a8Q+Jmth94G/AqinTTJ0MIHzOz3waOB66miOC8otz/YuBnQwiX153z2ss+PzrupDvPdd1CCCHE\nnNn16ts3XTKfb2mPOD3b0fc21wJgM7stcB7w8hDCG8zspiGEq8unzwNeCvwjsN8dtp9C4NRy8V3O\nBuBB/cDbczvq654Xs0ZmfGdTlgzNS5+7/1cu473ffhLtfa5VeSWJYvgOoWOrtqeVm8T+SSv7XS3L\nTavuo9Xj90f7rd7ihI3t7i1uXj1xs1ttbPZudpvomGuP+/aN7au45cb2/xw8Ltrvf66p1nTl1dW/\nsW98I7ZeuObqqsD4+msP8pfPuiXnPPvrHLyhenztxrgIee1gdd+3ofdTWwcXvfJiP6q5Sf79pzU0\nk47fCQ6cfwb3OPsDO/qaexFdhwJdh4K9eh0OnH/Gbi+hMcyzAPiWwIXAL4YQ3lc+fIGZ/VJZ4Hs/\n4GPAAeB5ZvYC4DZAFkK4al7raio+/eSLgYHagXppmmlWd+1hTdu293Bqr90QHeOdtldXqv325fui\n/XzayXc2rSQCLep0Ko/pdHN6a9Vae4k5ZZyCmm0ezaxmlWrhFkIsIkN5M23J0ynSSM8ws2eUj/0q\n8Mdmtg58DXhCCOFaM/sgcAlF886T57imhSOdAOw/dodun7r6GagfqJdGE+pm0AzW48hFPIOminZk\nhyrB4qcEQ9Lp5MTMah6fe58brneM62y6IZ1H48TNetm23V3JWT80eYIwVPNogGgeTXtKlCUyq6yp\npQHV0wghFpOmfL+am5gJITwFeMqEp+4+Yd9zgXPntZZlYNIwvQ1qBuptjsx4AdOfuA1TbA98y/Za\n3JrdcTNooknBWTKPpuPbtivBsWkeTdS2XWx3uu1ouN60QXu+GHiYRF98lOVoRmlALdxCCDEPNDRP\nCCGEWFKa8p1KYmYHOdpt2rNSNx14VkPKze7aLjITeTi5lNN6Yk7pJwX7+pl98X77vO3BSsdtx1GW\nVZd2OlSmllZW2tFwvfVk3W1XQ5NF24mJ5XBy0W9dygm218KtKI0QQhwdJGb2ID5lNKtnkyets6mb\nDpwaUsYzaOo9nHwNTVQ/47azg3HNjK+hyX3KaSXeb7Xt5tF0vDllLDi8p9PBlUrMrKxWf9K99cQC\nwaWZ2v795cl1qCkO9imn7UwNhvquJyGE2A2aUu4nMbNgTLI6GPVGUTnqrMXAm4frTY7aTPNwGhya\n3NmUOm1nroam7YbrdfuJ7YEzqNyXV/Uz+1bS4Xq+0ynb+Nl1+3WSgXze38m3Zg+SWpi64mAvRI72\noD11PQkhdoORupnEXiV15PYFwaNscsoJ4g9eXxy82cPJPdeb7LTdTpy2M+fh1K4xpwRY6Vb7rbqU\n0zHdeCaO93QaC5vVlSxy3T50KCkAXnORmZooDcSRmpmiNBBFarbjwi2EEGL7SMwsMZtqZnzqpVN9\n6E6zPahLOU1z2m4dqgRMvi8WM6v96v5qdpNq26WcAI5xUZYbVotvFqurLVYO+ohN/Oe93nUzaFyn\n0yDpevKRmlmiNOWeG1venXtaC7e6noQQu01T/nuRmNklhkn0pK4gOI2yHGkNja+faQ3icw1rCoWn\numv74XpR+iluufY1NO0oShPXzPji4H37queOcSkngH3dqjh4LGyOWYEbJxQGj1lb9cXB1fH9JDJT\nV0/jozTtpGh4gIvgqFBYCCF2FIkZIYQQYklRAbDYdcYRl2F/NHEy8BhfEBwN18vqC4Dr6megfqCe\nTzNtctquKQ7ODsVpJp92Wum6Fu72sdF+vtOpaNtusW9lxD43XO/QahKZcTUzPuXUT9JRdcXBPuWU\npuh8aulIB+0V51c9jRBi/jQl2CsxswREqaq8Pk0VdTDV1M/ANNsDl3JKxEzctu1tD+Juptx5OnVX\nXcopaeE+xk0KPqbbATKO6Q7Z5wTMwbV43T7tFKeckjSTKw7Oo0nB9VYQUaeTM4uNUk5Qa4mglJMQ\nQmwfiZklY5ohpa+hqaufgcSssiZK098UmalqaNpuuB6Hknk0roam47qeVjrpPJoqUrOv2wVy9nX7\nkZ/TwcQC4aAbvOeLg32UBuJIzXBGMeOfq4vSFDseva4ntXMLIY6Upvy3ITGzR5h1OvAsA/XSouG6\nGTTpft7DqS7lBPVt23XFwJAM1zvo0kzJcL3WwSoy01m9bmN7ZWV/tN++ji8OXgFWOSbvRfNo9q3W\nTw1eW5scpYG4INhHofq9+qnBWbvary5KUzxXbdfNpoHZu56EEEJIzDSGaJjetFTSlJRTNDSvPTnl\nBGnbtk85TbFAcMP1fKdTlgzXa7u0k4/SdNevj/Zb7bi27XIezWq+zrGuy+ngSpxmOrhavd9IzKwl\nk4LXqvfhLRHqjCqL+66exn3VGSZfe2qnCB/FrqdWq6UojRBiJlQALBaeabYHdSknSNu2Z3Tarhmu\nlyfD9UYuUuOLg/PVZLjeiqunyYuU077sEKt5NVwvnRpcV0+TtnD3aiwRoveaFPYO+tU5Mve/Q3vK\n/xRDd4mOhiN3tJ9qa4QQS4TEjBBCCLGkNOW7jsSM2CBKQdXUzwAMXIQic/UzvpYmjcz0XZopX5uc\ncoI47ZQdcn5Oa3FkprtSpZ1Wy8jMKjdGw/UOuZQTxGmng1NauNddNKa7Onm4Xt6P/+n4qI2PhMyz\n60nt3EKII6Up/21IzCwwY/Ex6o2mTgb2IsX/3Wbpjq6Gpq5+pnhuclePr5mZZk7pO53aB5OamRur\nNFPrmMkpJ4COSzutdovt1f4N7HN+Tj7lBNQWB6+tx1dibb16rtebnHIaTHMcr/FzAsjy6tzDGbue\njmY7NyjtJIRoHhIze5BZO5tqj09qYaYVBNcdN6vtgY/GZHl9ZKbW9iCdR3PIdzq5YuB9cdeTj9R0\nV4rtbu+GjSgNbLZA8JGaQ972YD1+f/tcPU3PC5uaKA1Av2Y2TTpcr+dESjsawlfv9XS49TStLFM9\njRBiJpryX4DEjJjIrJOCR8PJ24O0A8pFLnzKqb0SR08G0XA9F6U5GEdmMjcpuFOmnDpr17PacfNn\nXJQG4BgXqTnYrf70N00KdpEan3JaX68EQr8Xp7AGNfNoZu162o7X09Fo55awEUI0AYmZhjDL/Jl0\nv/pYADNPCvYpp6lTg2s6nYa9XryfH67nW7gPxpOCMydu2mXKqb12A93u5lqaMfvyygLhGC9mkhbu\nQ1ELt4vSuJRTP0mj1c2mGQxikTIcuu6oGiEIUwbvzdDOnWUt1dYIIWaiKd9hJGb2OLO6a089x4wz\naOqO+f/tnXm4NHdV5z+1dfd9l4RFwEdAXPmhMhgBCasJCoKyRJQRRhbBAWREEXVGZHESHJcBFRcY\n0QEh0cdxXCBAMqDoQAAjBEWRRf1hZBAfhEAS8pK89/be80dVv3V+v65f3bp9u+/t5XyeJ0+qupau\nrn7vre8953vOqesUPBLRijirmecUMAcPu66YSdrCHCz8NMkJ1yg8EebgqZ8m7p4la896aabsiLTT\niayM0nS9Eu6uiMb0dqSYKYWJjNgADAcyaiPFjG8ADkW1mgmMpuXcsTAX66gERVFCbEqfmRkPqKIo\niqIoyjqhkRllX/yxB9JDE+oUPPHSTG6lU41RWI49kCXcu94Mp51ZP020d5akXY5AaLW8NFNSRmZ6\nIuXUbXmRGTn2QIwwcLw0Ay8yM6z209RFZlxvjZuOkpGRWHhmmpRz72sA1rlPiqIULO9n++BZhMOg\nYmaLqZvhVOefGY+rK51CVU7gVjoNe6WASVrhqqfhnvDMtL0SbtkpuEgtTfbOEnd2zr2eCWED0M7K\nbTutcvmEV8Ldk0MoB8I/I6qeBgNXrMmqJylmpMgBV8BIP4300uTr1b9gZDl37P30TgVjFEVqFFYU\nZatQMbOB+CJFGoIP658Bb1hlYLq2b2h1IzNittNMc73SQ5O0qqM04EZqonYeZZns7RKL/jNJ253n\n1MpkD5py+UTSdvbrZaUY6TlRGuGZGbpiRnpoXP+M31yv2k/j3y+5Lu+QHI/gO2amRuEojuea+6TC\nRlG2j035EVYxs2YctgdNHaFKp8R7H0csCR3glGb33UdtJNIjMkpT11wvFKUBN1ITd3JhM97bI9qp\nabTXKiM1HRGl6XfcfjR9Eanpt0oBI6ueegP3nshIzXAoq548I7QTmQmLGRnBCXUUnukuXNzj/F4L\nAePvJ5ZDRuGmFVCajlKU9WZTihtVzCj7UpeOCjXX8zvaOl6RYXUZM0Di9KOpjtKAG6kZFyXc426P\neLcUMHHbFSlJuxQwLSFsdrzmen0RqemlMkojGuh54wz6A9mbRqScvP1GckhnbWRGRk9Eo720uk+N\nJEkSp0/NxPtlFYrAzFMBpSiKsgqomNkCQj1o5u0UHDp3yBgM3giEkYhi9Dwxk5XRGNn6fyYdVeGn\nGe11iVtlVCVqu5GZqFWKljQrl9uZ21xvJxFRGylmRJSm3/HSTENZwl0dpYFwCso3Csv1UEfhOCA4\n4jRp5K3JNzZMLWkKSlE2kk35MdXSbEVRFEVR1hqNzKwxU//MeDA5Mv8MhCudQlVO4DbXi5LqRnvg\npp1CKSdw007TrsGjbo+kXT3bCdy0k1P11HKrnnZEmmkgIj39VFQ5tbxJ22Ju02BYfvbhyP17QUZq\nRtJjVBOZcT0z4T+jprGrOEkaGYWBRgMt893UKKwom8imZJRVzGwZdWMPDlvpJB/bM/OcRNopNAIB\n3DEIMrUkU07gips4y8XMcLfnzHqSs50Aoo7oGrxbChiZcgJoCQ+NFDauMdj90RkI0SL9NP2BL2ZE\n6mwUFjMhAeMsewJhup6kyVwdhQ9bAZVfnxqFFUU5elTMKAcmJGBCURoIj0CQURqA2JnCXQqduGYK\n97TR3qjXZyhGIMTeEMvorDAHi3EGccsVM5n008gRCB0RsUndQZODtjAHC2Hjl3APHdETNgo7PXuC\npuHqH980S2vFjFMRFUuREa6ACkVtfKOwRm0UZb3YlB8/FTMbwlGVbEN4kKUUOTPl3LIHTSBKA26k\nZigetEm2fwn3qD9kJCI2w7Ne12CRJopE+mim6ikrRUtLRGN2knJ54DXaG4jIkRQ2/aEreoZC1Mko\njRQv4EVthlLAhIXE1PSbZMlMEz5JSDyMnISUZ6fTdJSibCR1qevDoR2AlSNi0c316s49DpRwzzzE\nhzJqI4RNz43MyLTTsNs/9/84LR+giZcKkhO5I5GCilpuc71IiBmZggqln8CN1AyFkBh0/MiM6EEj\no1XeOAMpZpyUU41/Zrotj8yE9wtVQTnvP+O0EcJEDLj000yLTEepsFEUpSkqZpQDEzIHy8eV/6gK\ndQ0e+2MPErmf8M94+0lxMxUwo/6wvtFellYvt9woi1xPRDpKRmlGiXvMUBiAhyICNPCMwsOxNAfL\nNJM3y2q8v7fG99lMIzOtjhsNamIa3g8pbuRMqDrBUde3RudDKcpqoAZgZWUZe1GRw6adFt2PJhSl\ngbCfRkZp8muaNQqP+kPXGOyZhl0BUz7wZ4zCYpxBlO0vbMBNQQ3F8aOsRszsiMjM2BUzcn00kv1o\nZMTFOeScaGm16iMzIaSw8Y+JAn1r/A7Oob41ceyZzTUdpSjKAlExoyiKoihbyqb8XaBiRjlHXdl2\nk2OCU7e9baGUE4TNwSNvFpKc7zRdHg3GTtVTXW8ap+opc38MZGTG6SgsvDRZ4qZyxiIyMxKhi1Hi\nlXCLSM1QRF+Go7BReDSqjtKESrM7J1pO6LhuVELYjxOOkDg24Tm7CzeZCaVRGkVZPpsyukTFjHJg\nFmkOliknqCvh9jwlcr5TPyr+P3Q8N3W9aaJUjENI3P2cNJPwv8TC5CsrowAykXbqCKEzanvjDKRx\neSLEzDjsmRmP5YNfPOwn7rmnoqXTSWt/Qc3z8B/2B5Wvz9iEQymoGgOwDrtUFOWwqJjZAuYp215k\nlAbC5uCmJdx1U7ijWERmanrTTKueAKfqaeiJmbglKp3ENlfkuJGURKy3pJjxQhdS3IyEsBm3fTFT\nRoFGUtgIAeQ/26d+ms5O2jgyMw8hYQPhqM083prD9rCJokiFjaLsw6b8iKiYUY6VpiXc/hRu2Y9m\nXDwAx4OR05smiv1ybiFgaozCMgXlipnyxyXxxIyM1CRCzLS9NNM4lubgctvYS8yNJiJCNREpLKfK\nyYtcFJGakydT5xdUKB1Vx7jhb7h5hA3UR23OvbzgHjY+KnQUZXNQMbNlHDZKA8360cyIFLFcV8Id\nGongT+EeVzSVGw3HTtXT2Ct3lmXb8mHoi5lQCkp6a2SUZmY/IXRSz1vTjoSAiUSUxUujDYXwGrdl\n1ZP0ivhiJl8/eSJmMnE/k7NfIAUlX583j37YdJQUGIvuYeOjvhtF0ciMoiwEX/Q0HVwpZdDUJzMZ\njR2jcBTXpaZklKYf3E+KlEiInsj32QTETBK7+2VifSKiNiOvN8xYvNcEGaUJe2amKahTJ3DEjP9s\nH4/d91oW80Rt3JLyw41UiOJYhY2i7EPTKOyqUx3fVRRFURRFWRM0MqMcmJA5uK7KKVjC7e3XdAq3\nPMe06mnUHztVT/5E7pCfRnpp8m0yBSVSTnWRmcA2f79UhiFElGYcuftNZGpJppycyIxzCJNJBkSc\n3pkwEZ6b8Uw6av8f+0WXazaN0tQW+B9yPpSPjlRQlNnmm+uKipktZtGdgp1zN+waPLOf3CaWI6+E\nO5azggo/zWQ8mal6koT8NH4/mlAKyvHWeB1tnW1CwCS+6Imrt7W9dNRE+mnE4MpxKsWMJxiJgBan\nd4aMJ2lwP/cuh/vWLJORX900vQYhJOrmQ4WETb7XuHg53HUYdKSComwSKmaUQ3HYEu55joHqqqfx\naOJUPfkTuUN+msgXJo5RuNpnMyNmpGgR+/mRGccoLKeCe2KmJaM20mfTElED797ln7bFqVbPq2by\nf8zFOZz+Ns28NL5ICG0bROFoTIjxKCxGg1O9A94a3zOz6JEKEhU5yrqyKf92Vcwo55in0qnxuRs2\n2gulmZpUPU1GE0YzewbeRzzYht5DTqagXDEjG/J51UcNxYyTHhHRl9irXc7kQ9N5gAoh0vLSR2kE\nnOZU2vXSTP79TgLbwsKmrsTZ2a9G6ITOJ5ebDr4cC9E69g8qxEgURUvtQizRCI6iHC8qZpSFsYiI\nS+i4JlVP4/G4Mv10br+Kcm6YHWI57SgM7hRv+aAe7PoVUHHlfjNl34GHuP8wlA/aTIieSWAZppGa\nO3EquY162mJZXl8gCgUcx6+KsSeMHM0i01TePZ4U5etxmjTqZwPNy77d99FxC8r6c8gemnNhjImB\n3wC+EegBz7LWXi+2/xjw5GL1bdbal+13ThUzSiXHFaU5jFF4MpjUTuSeje8U+81EZsQ54upYgf+Q\nG+z2xLYaUSBFi9iW+L6PQAQni8IP1yknB2eaZowICZt4JhIjxJroleOnbpzPHoXvg7utOhI2HIT/\n3Y3k8X46UbxnqOw7X29mKJZoakrZNI7p3+F3AR1r7YOMMQ8Efhm4BMAY81XAU4ALgQnwXmPMldba\nD9edcGlixhiTAK8FDPnvl2eS/+l3eXGBHwWeZ60dG2MuBR5D/sfXC6y1H1jWdSmKoiiKcqw8FPgT\nAGvt+40x9xfbxEHMwAAAIABJREFU/hV4tLV2BGCMyYDu7ClclhmZeRyAtfYhxpiLgVeSi5mXWmuv\nMcb8JnCJMeZfgIvIVdjdgTcC37zE61KOgKbpo6Y0qXoaDyeNy7mlUXimhLvB9dR5Q2ojM4HjZs4n\n/pqXkZlwX1+Yfvp294xTFdT0pzyOxITwKGwajiNpYg6fz42+NL1fTb05ouIsUPadJMmhq6Pm8dlU\nHVeF+myUVeCYhmafB5wR6yNjTGqtHVprB8CNxpgI+EXgb621H9/vhEsTM9baNxtjri5W7wHcQB59\neXfx2tuBbwcs8A5r7QT4lDEmNcbcyVr7+WVdm3IwjquEu6kHZ7rfZDA5cDk3uNO5gWCvmlHN3KeQ\nZ6bOcxE6HiCN4spt8i4k3sOwVay39m5xz93xflsFUlBRFP6tFgtx43p96jxB8njvfOKFrvQ6B9JU\n/rbRoKbqqfDJJFlaWx0VNBHXlH1LmnQh9tF0lKIA8EXgtFiPrbXnfgqNMR3g9cCtwA81OeFSPTPW\n2qEx5grgCcATgccWogXyizyfXKHdJA6bvh4UM9/yoas47973BOCxQ7uEK18v9B7kPOLTHz3uS1gJ\nTj3okmN89ySw3PZ3XDpv++17H/l7riLXXnXRcV/CSqD3oZrQrLYlcy159uYPC8/MR6YbiojMW4B3\nWmtf3vSESzcAW2u/3xjzQuA6YEdsOg3cwqxCm74e5D0XPA7IH+JXp2ah17tuHPc9OGyUpi7iUlfC\n7R/37Td8jHfc5RucY/x9QtuSzO8FI1IqmUjxtMr90rZ7TNoWU7Nb5XK244ZBUjGDKTtRPuDTE+7D\nPjtZ/qhkp06U5z55slw+fco5Jjp9Hp1LfoTuW17F5OR5514fnTjf2W8g1nvtcvls63bl8vikc8zZ\nYXk9t/bLa7216/4KuW2vvF+37Yrj99yIxO7uWCyXYZGuaGDY77rRr57YNuiV2wZ9d7/hYMgbf+2r\n+Z4f/WeGg3LbaODuJxv3jYWJWEZPRl5kJzQ7qi56Ivdr2lm5aUm4c0zFNVx71UU85HHvrth7u1jV\n+7AKAuuYAn9XAo80xvwlecD5mcaYHweuJ/8r6CKgbYz5jmL/F1lr31d3wmUagJ8G3M1a+wvALrll\n4a+NMRdba68BvgN4V3HxrzDG/BJwN/Jw043Lui5lfWha9RQcqeCfTyzP462RTfhGM5U2TTukLI+p\nvJrc+kUi8dBMan5bRU4vc3FPW17qLRXbxH5x5IqwRJQPSW9NkvjVWjIVJ44XQtI/JlQdNVuNlq9n\n7cwtk/crqkSq0BU2zVJTEznB/JgqpSShNFUURZqqUlYKa+0YeK738j+K5c5Bz7nMyMybgDcYY95D\nnqV/AfAPwGuNMa1i+Y+ttSNjzHuB95E/Y563xGtSFsxhS7ibGoWbeGsmg0kjbw00H5XQtAmfRJZ2\n+yJHRn3cY8LejKhBObZkdOttge4xOYkQMI6YEQ+8yBvYEgtxk4j7FUfeflH5O8itQveiX7L7sRz/\n4LzuiRRxwkQ0Lez5+xXnaHUy5xi/3DzU50f2txn5x0hB62ypaet4SA/OvL1uJNr3Rgmx6Dlsx8Uy\nDcBnge+t2DQTV7PWXgZctqxrURRFURRlc9GmecrCWESjvXm6CAevp+Gwy7q5T/NEadxYjPsjFmrC\n15RJzYjbaapjeOttzijc2C8vdraVnz0LRWyASPw1H7fKmEScuvGJRFREyeU09rxDoWiMM4jT/b7k\n+q70NQUiOJ2dlpOqGvTCaaZQsz4/KiLTUfKYsTc4s0k6aiaqcsh0lE/T4ZnOMRq12To25TtXMaOs\nJSE/TZ0YmmfuU0jY+KMS/PLuKcfhpBnu7jnrMz/kMp0kBzEKAZON3YdzJNbjiVhuufvFaXUKSqaf\nAJK4JZaFsVqID78rcppWC5hZ0ZMfd/J0m+5uPPP6uc8k/TRJtQfHLwGfJx0V7nXjCZE50lHu4dXl\n4f7AzTq0PHz7qPn7aK1QMaMshUX0pmkapZmKlPFwEhQ2/jnmMQpLYYM7molEDH0MCRs4vLhp8lAa\nnN1zK228Y1JpDh7LaIy4JxP/GBGRCCwDxG0ZtRE+m8jdLxW+olQImzQRVWGez0aKmTStjuzk2wox\nczJztvV6ftVa+Z31RaWU9PMMvbldsjqqaQQnZCgee8bzeSI4zsueyGkSwTmsyAEVOspqoGJGORKO\nwyg8TwUUhKM2QWEDjrg5KmHjM30ADm7rum09fYOffPg4kRlx77wHsFyPRjViZixEgRA2SeYl3zKx\nLSrLvpNYlKvXpKZSEY1Jk2rRc+pUek7Y5O/pXkOockoOB417bndhKYDkMcM5Ijj+TKmJc0x1mipf\nDwgdf75X8a/Xn5+l5mJFMt6Q70zFjLKWNInaLLK7MISFDYSjNlLYwHzpKPnwkpO/Qwy7btio7qEk\nt6VSwNSJGSFgkpp0lJOaGntColWuJ2m5nMXlMamXmsoS0aMnLX91tVL3HmfF+u3Oi9nNZDSnOoIz\nsyz6DvW8c8ueNtKDM9sRWgiTUVK538j32Tj3WHSoxifwL9H7nqNC5MVJ4ogM9eMom4iKGeXIWeZE\n7nmYMQCL5ZAAauqzWUQ6ajJuVpp9LjKz269PUzjHyHSUOMZ78CTiwRuPhmI5LHpaIxGlGbkRjmRU\n3pikXW5LUhmxcc+dxaW4kampVuJHcGIg4vyTE7JAaipfl9uqIzi+H6cXiMzEnuiJhdCRzfqcUnHP\nwyNFT8hoDK7ZuEkEJ4rjpflxfHRcw/qxKff/YA0sFEVRFEVRVgyNzCjHyiKNwvs1zavz01SdD5pF\naWb2k68vwFvjsr/TZthz95ntTjupXB4PxTV4f2FPRDQgleZgLzITDUU0RixnQ6954LC8EdJnI6M0\naeZGc7JMpqPEuIfEvdYszYAWtz81pCVSRn46qiVGVYTSUamfwhIjLbp7wsPjjcToZ+Wv1oHw3cR9\naSB274m8/yHPDbi+G+lzCpWHx2mycHOx8z6amlprtGmeoiyBRRqFj0rY1O7nv+8hvTUu3sOw8NMM\n9ga11Uyh1FIqHoZ+Pxvpp5HHJ94DORnJdJQ0DftppkHltkSInLTj5ujSltiWCqEU7zj7teIO0OJ2\n7T2ymnRUJoSKTEdlUgC13O95r1vts/ErpVIhKHsBo/HQS3sNZSovlWkqL5UnKqykzyZUHp4kycLN\nxc71HENqauYcKnrmZlNunYoZZWNZxKiE0PlmPDML9tZEgbEH0gA8GbsPw6TYNjpAZMZ9vVrkgBuZ\ncZb9QYxiXQqdeOCKmWhQHcGJhJiRywCxEDdpu3duOctOO/vlEZzzOT+7jVZS+mxaiTtHqpWW4qYt\nIiltEbFpeyJTru+K/bpdd79eq1r09MUQUlkODm5F1ECKnprycOmziZNqQ3HWzlwPTqAHDhx+9pRk\nmdEcH/XjKCpmlJVl0UbhRUZt5jENz+wnX284HyqRr/er+5eMhmNk1MYXPc71CHGUBdJP+Xq10HFS\nU0AqHrRS9CS+UViknZzlgRAzA0/MDEsBkw675bIXwcmyLnBXzhvdRJaWQieLvAiOFDqpiOA4Ise9\nd23x78YRNl4EpysMwG5qqvysaeY+xAc9kcoT79v3poKng3KbFEAzaatC6GTtVrCKyhcLIaEzV0+c\nOaI5sFihE5q/BSp0poT+uFk3VMwoa8EivDWSdUpHhYRNPK6+nlF/5Ez4jmuESdqufhClnv8iJGBm\n9hPpKSlmxl5kJhXrExml6ZeCJRLLAMlAbKuJ4CSdXOic2LuJtFUe08pOOfu10pPnltsiVdUREZy2\nEDkAHRHBOSvESCvz01Gl4Mic/cKpKSl0+kKwpF3Pj9MPRL+8cQ3TKqqslTqVU25kxxUEIaEzT0+c\neaI5sNy0lXO8prA2ChUzylqyyKjNIhryhc5X92u16UgF2QI/aZcPttlz56+MB2Mmo6b3RJZZhyM4\nrpgJ/2XvbDsxqnwdvKiNeLg6D2ffNCwiNU4Ep9/19svXW7feeE7YgJuaAsik0HGEzYlyOXF73ZyV\nQicrIzidlnvv9loyVVV+F3vi+9vrut9RW2zrdsv70/OiQz0RwRn0RQQnc3+dT0VL51SHQU9GhNKZ\nfaZIcSO3+d+zFD0hE/K8HY4j0QSxaX8cyThQpOuLH+1+nKNN8xRFURRFWWs0zaQoK8I0SjMeTI7M\nWzPvRO555kO5CCOnd22TUX6WUX9cW/YdMhEnzuue10eklsYN95Pbkr4fARD+EJn2ECmn1EtNTXoi\nMtOXkRkvzVSsJ2duIhZRm6TjDeDs7J5bztqlt6aVlVGaVuqlpmQ6Ku2IZTcdtRuI2uyKVNBe2/3W\nd0WAqd2Ogvu1e+U97okUlIzYQBm1OXGy7URtZMRF+m/ybSLiIlJTfjqqSUVVPPH/bRys2R+A3OKb\nlUNRkVAEJ44jNR5vMCpmlI1iFUzDkkXMh3Lep2afqc9mPB471VF+ZVTIa1Pvs5EPtnCKIFQSPtMD\nRT7YOuLh6vhsvLJvIWZSx2fjGYWL9cmZLzgpqNhLR2UDIXT6pdBJO6WAyVruMVLotEVqqhO76Sjp\nu9lLy2Xpudn1UlMdaSgWoqfjiZmuEDNS6EiRA6XQOXW6TV+IlH632kAMrtk4ZDQGGEkB4wig8IDN\nsUgfjZ1S/7C3RqZADltGHsXxof04PvP0zlk1NDKjKCvOcZmGnWuYcz5UyJ/TpOx7MpgEDcSzxwnx\nUeOzcaIsNZEZuT4aSKOw760ZB5arIzYA434pYKTQSX0xU4ie4Re+QNwTYqbneWuEuInae+L1ctmP\n5mRtEbVplaKn7ZmLO5k0FMtoTilsTmReNEeUbe9Ib41n7A0Jna4vZjr5Oc6/Xdvx4PTb5fv0vDL+\nrCea/TkN/vzycFFFJYaGOuZi7zuXAig0ugHCxuN5ysidc0VR0I/jTZYIipRFm5CVxaFiRtkajsM0\nPHMNDUTKzDGB10OpqfFwAuJ9Jmn4WqepKQj3tsm3VV+f/8td/hKP03DjPicyE1ge+SXJnTJ1I43C\n456XZtrJ1wdnvngu5QRuZAcg7goxsyPFjHi9t+sck3RKMZMKoZO13P3aLWEiFkKnk5Wvdz1zcUjo\nSJEDrtDp9kXayhM9e4W/+XbnJ3Q71VVU3ZlKqfJ76guh0+/7KaxqoTMcpJWvgzujaiRESl1FlZPC\n8kRPPKkW1aHITtLKwrPIFtAJWRIyIa8iGxKYUTGjbCfHlY5yrmGO6qgmqam63jZyP2hWAg5uamoy\nkg8Iv0KkWQRH/tUu0xRpQNj469KDI9NUclv/zFk3NeWLnk4pHuJuWdkkIzjRjtubJhYCxhFAQuSA\nG8GRQkeKnI4XzdkR0Zw9Ec3Z8fw4JzKRwhJRFlkpBdDtR0DEl5w/YbdXfn9dIWb2Ou73J8WMFD2+\nH6fnRHBE1EcIoKEXmZFRm5EjgA6ewgI3stKkpHzeTsjO64f07cDqjQ/QNJOibAjLTEf5NDUUO9dz\nwNTUeDiZq3HfqIG5GNwIjv+LMM7EA6KhB0eWhIfSVOCmqkJpKhBi5tZd0kEZzRn3wx4cZ1lEc2T0\nBjwx0y1FSrKz6+13ViwLYRMQOeAJnbRc7oloDrhCpyuETTdzxzXstTOgzR1PDzjRqU5b5YIHsV69\n30xPnG55zwfie+p1Za8cL5pzyBSWL25D0Z1QZMfvhByK7OTrh/PthNJZMJvSUhaDihlFURRF2VI2\npfJKxYyieCw6BSVZZDoqFAGaDCaNm/WNAtfTtCNxqHEfuIZiWQEFbkl4NJBRFhGxSd2zO+bgGm9N\nUnhM+rd1nW2pn46S0ZiuXC5TTjIVBZDsiHSUiNrEe65RWKanEidKI18Pp6ZaYrmduftJ301PRnA8\nD04etWnzJTu30RUenD3hwdkbuI+Avb7044jycD+CI6M2/fK7dVJTXkuAnjAhD+QcKs+PE0pV+Q3+\nQqkqx2gsjm912p4JOezpOnwEp2bOmZqDl4KKGUWpYV2EzUHOPU+lVMhQ3DQd5ZeDh3w3Ic9Nft3l\nOZxKKc8rMhU9g91eraE4EQ91KXRCIidfrxY6SdsVMzIdFZ8Qqal2KTjinbPOMVG7FCbJjkxHeTOl\nhNDptMrlvpeO6iUngDty+/hmeq3yfbuiP07Xq6jKU1PF8UMhevpVfpzpNuHHkWLIH765Iz041Wkq\nCKeqZJoK3Cnjw4CwkcvtE+1gh2PfhJxk+6ewwDO8B0TPyCtRh3Cn7eNg1Tw886JiRlEa4ntrJKvk\ns9nPM+PsG3i9Lq1f1+sm5LuRIgfCvpsoFn/RtvxjyvUm5uLB3sD56z3JqkUPuEInJHKgJprTcUWB\nI3pkBKcjxMye65mJZARn76x43RUziRA9WbvcJkUOQLt1Evhaztu9gYEwF/dlNMcTSt2xFDphP06v\nI4VOudwdCD/OjjevSoienqjC6vbc709Gdxw/jmdClmZlGd1xpo+L7/Xk6U6w8mrkV1TNUXkVMiTH\nnklm1dI6q3Y986JiRlEWwKZFcGoNyWJ5VFOiXjcVXCqiw5qLI7+HTfFAHewOiIWAmel7EhA6UtjU\nRXOSVtn3JtnzhmK2S3Ej50PJCE6y46aF4lZ5jGMg3nEjLrRFRKhTbosDoqdz5jO0hGhpC9Gzk7rH\n9AMprH7ipttc0VNed29Uip69oft4cYROv5kJuRdYBugJEdR3TMjV6azTt9thOJACqKEJ2UlhHVz0\nzERzNkQ8rBoqZhRlwRyVsPFZZKVU3bnrhFIwVVXTPNAROgGRA67vJpYprMw991ToDHtDR+iMB+75\npNAZ9qSwKffzp4KHIjhx6p47acmScCFSxHDL1BNAsRRAjhjy/DhtKXpKUeGXkSdFSiu5+bPEMoUl\nRE/WcoVSW4gemcKSkR1wozt9mcKalMv9sRut6g7L9W4n7NsJiZ6e9/3JDKCM9LiRnfLfxh3u0HGi\nO/1+Jvbz++jsn7aq2yaFzcj3+oxC8dDjQUuzFUXZl2WmpnymQmIymMzdoXhKnUhxjq85d9NUFQFx\n1DSa45uLp0Jn2B0FozngRnQSIUZC3hxwhU4sjKrydXCFjhRAcSoiQB3Pj9MqH66xGHswk8JyhI7o\nldP2PDiF0BnddCOx8OpEIrKTdlwxMxH7pTKF5YmejhBHQxHNGYhIj4zsAPTF+8rITq/lfr7eSHQo\nHoZFT2+4f6SnJ8Z73fEOiSd6yn8bA+/ftyt6pL/HFzP7R3pm++islpjZFFTMKMoxsWoRHMkiojnz\nCJ3DRnMAZ+BmKJoDYX+O9OZEnpgJVVuNvFSJFDppW0ZwRDSo6w7SdFNYYrkuhdUSRuN2tegZ3Hiz\nsy2WAqjjprocg7Kz7KaZ0oBvx+mV4/lxhkLoyEhPblQukSmtnvDt9Np+pEeYlUfStyNSU+e+r4S7\n3H7sRXqkcdk5tSN6pNDpef6eviNmqgXQ0IvuDXq+Ifh42ZTIjLbvURRFURRlrdHIjKKsAMeRjvI5\nbGoKFj9vKnhMjW/HmR5e48FpUlHlz6saD6RXR5Tlxl5kJmA8lt4av7rKTUeJ/bzZTNKP40Zz3Iqj\naaqqd/MZJ1UlIzt+NMcxIYttkReZiUREJ5ERnJZMU7kRl7GI4IxE1GYnc6NDA9FXZyDKyPuJ59uR\nEZxJdQSnjNic5i6nd520VXdYXYUF0B/IVJVMYeHtJw3KcoBnuPS831+tNNN4QwzJKmYUZcUJCZ1V\nS03B8XhwQj1xRntj531l2Tg0G7g52x+nuhHgTAorYDx2zp26Ykb6biIhjmSayj9OLs+KnkLMnDlL\nfFZOAhfCJvOOkUJHenj8FJZIVUWtakMyLf8YUXklRE/WcsVMS4iesRA6w4ZpKyl6+ueGd57mzu2b\nnbSVNCjLKiyArkhb9cW4DV/0uEJHCqBwFZbvzzluNiXNpGJGUdaUkMgZDyZbFc0JeWsmg0mww7F/\nXKgRoB/NkTjCpMaPMwrsF3sG51FPbquutALPhCzFjGdCnm7r3nLWrbzarY7s+OuxjPrUiZ5AFZYv\ngBqLnlCkxxM944DokVGf0px8D+6w92+OQXkgIjv91D13X0Z6akRPf1wd6XHEzND9t+FXZSmLQcWM\nomwgyzQXS1YhmlM3cNM5X901yJWAyKl737oUljtxPDziQQodGdmJYv/zyQhOdUk5lKmq/tke0d6g\ncj9fzIQiPTNRpAaiJ5lJYVVHemJPzITSW1HLGy3RlqkuUaElRE/r3PKDOHHzpxgJg/JYRGmGXvfk\nYVpukwKo7wmqwUQInVa1ABqM3HvcddbdaNNxsCl9b1TMKMqGc5R+HMlxV1TVTQufOV/g9bqmgHWi\nR+43EkVLcVydcgJPzDT07cjKq2HP3W8qWvpn+0RxPPM6uFVX+ftW71cnekICaOaYgOiJA14f8NNe\nXqQnsE36eSLR0C/63KfJhACSZeh+qmsiIj11qa6RiOg0jfpIAQR3RVkMKmYUZYupEzqSdUpbyX0W\nUUYuOahvBwj6durmWkkOK3oGu4Og6PGjOSExIyM7EE5vhUQOhJsMzqa6qvvtxL44EiMWHNEjjxGv\njz53g5PqigICKD+HnLtVHfUBmLSqRY8jgDwxM0plhOn4xYzOZlIURVEUZa1RA7CiKFvDKlRUSY7S\neOycL7ShpsFf0ITsHRPy5xw2gjPsjoIRHJmyyrdVR3DqSs+lpycUpZHX42+bTWEFDM51qa59Ulin\ngO7nbmqewhJRn1A6K98mDcrlNhmxybzJ5BMnuvNAlMWgYkZRlLlZVz8ONEtVNTUhz5w7tKGmP86i\nRc/UqzPoDoNenboqrNr9AgZlWZE1I66k+HCEjTcKIiCUZsRR0KxcLYb2Pn+Lu59MU82ksKo9PTN9\nedJyv6CHxzMuR54gOm7UAKwoilLDcftx9hMehzUhS+YRPbU+nQWIHqdEPeDVGblWmFqDsrOf49up\nFjAzAigZVR5T59up309uq/bqSGHTveVs0NMzOyi0upJLCqCZ/UICKPON0KslZjYFFTOKohwrR5XC\n8mkiOBYZ5YEFp7agkegZ7fkDNsOfaZGprrqoj2RYZ3AWaa/EExyRI6j2F0DdM3uNBFC+3szU3CQl\n5gsgecxpjp/JeLU6Es+LihlFUVaS44rsSI7SwyNZpOiZec8jSnXVRX2cYxpWa42aRooCAqh/W7+R\nAIJwN2Z/BIUUMKGUmB/18QXRcaPVTIqiKCtAXSdkySaKHkmobHzukvSGokeyiKhPqC/PzHGBKJAU\nQLKLTu/WfviYJJzCkubn2BMzzn4BH1AU+54g7QC8DFTMKIqiKMqWogZgRVGUNWKd0laSw0ZzZsY6\nzJHCqu2ELDmiaI5/DU2iOcPuqMbT4w0hDZqavY7JSXU6Kg4cn++nkZlloGJGURRF0FT0SFZNAEFY\ncMyVwpqjWmseAeS/V0gAQVgEjUTyzDlXLzw13eewVV3O+9R4glYBbZqnKIqiAKsR9fFpWqIuOW4B\nBDUmZJ8GA0rluRZR1eUTur6mYkhZHCpmFEVRjohVi/r4LDINNo8A8pknIRMSQ3VVXT6TtNk9P2h0\naBXRyIyiKIqydOYRQHB0ImjeNNiUuujLYQWRFEMHuc5lRYdWkfFE+8woiqIoK8pUBG26GIJm0aF5\nhdFho0M+TQ3dysFQMaMoiqIoW4qmmfbBGJMArwUMed3bM4HzgauAfyp2e4219g+MMZcCjyHvcfQC\na+0HlnVdiqIoyv7MG9GZsmpen3mHky7C+yPRwuzlsMzIzOMArLUPMcZcDLySXMi80lr7y9OdjDH3\nBS4CLgTuDrwR+OYlXpeiKIqyZA4rhmC9Ul2SoxRHh0UjM/tgrX2zMebqYvUewA3A/QBjjLmEPDrz\nAuChwDustRPgU8aY1BhzJ2vt55d1bYqiKMrqswhBJM+1ruJomWxKB+Bo2R/EGHMF8ATgicBdgQ9b\naz9ojHkJcHvgFuAma+1riv3fA/yAtfb60Dm/+NGPT8679z2Xet2KoiiKsmSO3Q18yX+ySxEBb3mN\nOdLPtnQDsLX2+40xLwSuAx5srf10selK4FXAW3AnoZ8mFzhB3nPB4wB47NBydWoWfs3rhN6DHL0P\nOXofcvQ+5Oh9yFnV+/DYoT3uS2A83ozS7KV5kYwxTzPGvKhY3SUf0PomY8wDite+DfggcC3wKGNM\nbIz5ciC21t64rOtSFEVRFGWzWGZk5k3AG4q0UUbuj/lX4NXGmD7wWeA51tovGmPeC7yPXFw9b4nX\npCiKoihKgRqA98Faexb43opND67Y9zLgsmVdi6IoiqIos0w2pAOwlrwriqIoirLWaAdgRVEURdlS\nNiXNpJEZRVEURVHWGo3MKIqiKMqWopEZRVEURVGUFUAjM4qiKIqypYw3pJpJxYyiKIqibCmaZlIU\nRVEURVkBNDKjKIqiKFvKRGczKYqiKIqiHD8amVEURVGULWVTPDMqZhRFURRlS9HZTIqiKIqiKCuA\nRmYURVEUZUsZb0iaSSMziqIoiqKsNRqZURRFUZQtZVNKs1XMKIqiKMqWsinVTJpmUhRFURRlrdHI\njKIoiqJsKZtSmq1iRlEURVGUI8MYEwO/AXwj0AOeZa29Xmx/NvCDwBD4WWvt1fudU9NMiqIoirKl\nTMaTpfy3D98FdKy1DwJ+Cvjl6QZjzJcCzwceAjwK+AVjTHu/E6qYURRFURTlKHko8CcA1tr3A/cX\n2x4AXGut7VlrzwDXA/fZ74QqZhRFURRlS5mMx0v5bx/OA86I9ZExJg1suxU4f78TrqVn5rFDG4nl\n47yUlUDvQY7ehxy9Dzl6H3L0PuTofajmL666KNp/r4XzReC0WI+ttcPAttPALfudUCMziqIoiqIc\nJdcC3wlgjHkg8BGx7QPAw4wxHWPM+cDXAR/d74TRZLIZDXMURVEURVl9RDXTfYAIeCa5uLneWvvW\noprpOeQBl5+31r5xv3OqmFEURVEUZa3RNJOiKIqiKGuNihlFURRFUdYaFTOKoiiKoqw1a1eavV8b\n5E3GGJPptLx8AAAKWUlEQVQBrwe+AmgDPwv8PXA5MCF3fD/PWrsZwzb2wRhzZ+CDwCPJ215fzpbd\nB2PMi4DHAy3yn4t3s2X3ofi5uIL852IEPJst+/dgjLkQeLm19mJjzNdQ8dmNMZcCjyG/Ny+w1n7g\n2C54SXj34QLgVeT/JnrA0621N8zTKl9ZfdYxMhNsg7wFPBW4yVr7MOA7gFcDrwReWrwWAZcc4/Ud\nGcUD7LeAveKlrbsPxpiLgQeTt/2+CLg7W3gfyKsgUmvtg4GfAX6OLboPxpifBF4HdIqXZj67Mea+\n5P9GLgSeDPyP47jWZVJxH34N+BFr7cXAm4AXztsqX1l91lHM1LVB3nT+CPhpsT4E7kf+1zjA24FH\nHPVFHRO/BPwm8G/F+jbeh0eR92e4ErgKuJrtvA8fB9IianseMGC77sM/A98t1qs++0OBd1hrJ9ba\nT5Hfrzsd7WUuHf8+PNla+6FiOQW6zNkqX1l91lHM1LVB3mistbdZa281xpwG/hh4KRBZa6f19Y3a\nPq87xphnAJ+31v6peHnr7gPwJeRi/t8DzwV+j7yT5rbdh9vIU0z/CLwW+HW26N9D0YNjIF6q+uxz\ntYhfJ/z7YK39DIAx5sHADwO/whbch21lHcVMXRvkjccYc3fgXcDvWmv/FyB9AI3aPm8APwA80hhz\nDXAB8DvAncX2bbkPNwF/aq3tW2st+V+e8hfzttyHHyO/D/ck99JdQe4hmrIt92FK1e+EuVrErzvG\nmCeRR3AfY639PFt6H7aBdRQzdW2QNxpjzF2AdwAvtNa+vnj5bwvvBOQ+mvcex7UdJdbab7HWXlTk\nwj8EPB14+7bdB+AvgEcbYyJjzJcBJ4H/u4X34QuUf23fDGRs4c+FoOqzXws8yhgTG2O+nPyPwBuP\n6wKPAmPMU8kjMhdbaz9RvDxXq3xl9VnH9MyV5H+V/yVlG+Rt4cXA7YGfNsZMvTM/Cvy6MaYF/AN5\n+mkb+Qngtdt0H6y1VxtjvoX8F3QMPA/4f2zZfSBPH7zeGPNe8ojMi4G/Zvvuw5SZnwVr7ai4P++j\n/LeysRhjEvJ046eANxljAN5trb3UGPPr5AIvBl5ire0e35Uqi0LHGSiKoiiKstasY5pJURRFURTl\nHCpmFEVRFEVZa1TMKIqiKIqy1qiYURRFURRlrVExoyiKoijKWrOOpdmK0hhjzHnAL5DPpRmS9yT5\nCWvt38xxrmcDt1lrf3+xVxl8v8uBT1prL2uw7zXAZdbaa7zjr7HWXm6M+ZC19oKa499lrX34Aa7t\ny4DXWWu/s+kx4tiJtTbyXnsG+UyhT4mXb7DWPuqg51cUZftQMaNsLMWsnreRd0y+wFo7NMY8nLzB\n3tdba2864CkfAlyz4MusYw/YXcSJ6oRMwcUHPN+/UTSvXCBvtdY+Y8HnVBRlC1Axo2wyDwe+HLjU\nWjsGsNa+yxjzTCApuqReVnQSPhfJIJ+w+/vAlxbneRm5qHg88K3GmM+Qdx7+7eL8Q+DF1to/McZc\nVrx2T+BO5BOcv418WvHfkQ+/mxhjfgr4XiAB/hR4IXAP8iGqN5ILmT8A/sUYczfyuUsnyVvVP78Y\nstqYaTTEGPNtwCuACXmU6j8A/7XY5zpr7YXGmMcCP0uehv4E8IPW2huMMZ8EriMfIfE04A+ttV9h\njLkH8AbykRK7wLOstR82xkw/+x3IB4I+yVp7w0Guu7gu+b4PAx4NvKC4vg8Cz7PWdo0xTwdeQt6y\n/v3AaWvtM4rjL7bWflJ+58aYrwFeA9yxuO4fsdb+bfHv4Az5wMa7Aj9jrX2DMeYO5N/5vYAe8OPA\nVwLfaq19SnGtlwF71tqXH/RzKooyP+qZUTaZbwI+NBUyU6y1b7PWfq7muCeQp3fuB/xH4GHW2j8H\n3gr812LA5auAd1pr7wM8kbwD7V2K4/8deaTjOeQP+ZcD9wbuC9zHGPNo8gflNxfXeFfgKcWxBniq\ntfaR1trXWWv/rLiGq6219ycXHg8NXPfrjDEfmv5HLr58Xgo8tzjXnwH3tdY+v7gvFxpj7gz8FvBd\nxWe7Fni1OP7t1loDyPv3G8AbrbX3Bi4DXloIhXsBDy5mJn0KeGrguqc8Xl5/EUXz3/dOwLOL815Q\nXMd/LgTfL5KnEx9U3Mf9uAL4SWvtfcm/q/8ttt2dXDg9nnxCO8B/A6631n4duZj7OXLB+Yhi+Cvk\n4vB3G7y3oigLRCMzyiYzJh++eFD+Evh5Y8xdgf9D/hDz+VbyhyrW2k8YY64jj74A/FmR0voX4DPW\n2r8HMMZ8mnwcxSOKfT9Y7L9D/rD/C+Bz1tpPeu/15+Qt2b+puJ5XU82zKjwzPm8FrjTGvBl4SyGW\nJA8APiCu4X8CLxLbr6s450XkD3GstW8jT+1hjPkJ4Fkm7yX/IOCfA9d97tpq0kzT93048LXA+4sW\n9S3gb4rzX2ut/Wzx3pcD3x56I2PMKXIx+YbiPACnjDF3LJbfUUTQPkoeWZp+zu8rPudHivfEGPM2\n4LuNMZ8APlGk4BRFOUI0MqNsMn8N3NcY45tNf774q39CPt9rSgZgrf0n8qjC75H/df6Bwn8j8dcj\nyj8O+uL1qonuCfCr1toLiujCheR/5UOeXnKw1l4LfD15OupJwFUV52yEtfZXyKNG1wOvMMa8xNul\n7nNVXh8wmC4UQy+/3hhzP/KhqDH5XKQrce/1QZm+b0Ke3preuweQDxP0r2sgluX3nInzdKfnEd/D\nzcX2LoC1Vs57GRTnAsAYc6/i38XryUXO9wGXz/0JFUWZGxUzyibzXvI0xKXF4DmMMY8iH0769+Te\nlK8qJujegVy4YIz5YeBl1to/An6I3AtyHrkwmT7Y30me/sEY81Xk5uD3NbyudwJPM8acMsakwJvJ\nU1WVGGNeQZ56uoL8wX3fhu9Tda7ryL0kv0o+oHF6rlFxLdcBDzTGfEXx+nPIDdR1vAd4crH8CPJo\nzkXklVS/CXwceCy5gDgs1wBPMMbcuRCpryH3z7wfuL8x5u6FwHiyOOZG4BuK5UsArLVngH8qJitj\njHlk8TnqeA9FBMoYcy9yf9PEWvte4G7kUaM3H/oTKopyYFTMKBtL8Vf144GvBj5qjPkwudH2O621\nN1hrP0aetvkY8Efk4gfgdwBjjPlI8dp/sdbeQp7uebEx5onA88nNwB8hf4A9y1r7mYbXdRXwRnLh\n8FFyM/EVNYe8Cnhi4YO5Enh603tQwYuBy40xHyQXYz9VvP4WcoPyGXIBc6Ux5mPkUZzn7nPOHwa+\np7i+lxXH/wHwjcX9uYY8SvaVh7huAKy1f1e8xzvJv7cE+O/W2huL970a+CvKCAzApcCvGWP+CrhF\nvP4U8jTYh8nL95/kRWJ8LgW+1hjzd+RRu6eJ/d9E7qHqHfYzKopycHRqtqIoG0fRt+biZZd6F9Gh\nFrmZ+gXz9C9SFOXwaGRGURRlfr4U+CzwfhUyinJ8aGRGURRFUZS1RiMziqIoiqKsNSpmFEVRFEVZ\na1TMKIqiKIqy1qiYURRFURRlrVExoyiKoijKWqNiRlEURVGUteb/Ax9FbYwgLYZXAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e98a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_probability_alive_matrix\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "plot_probability_alive_matrix(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>predicted_purchases</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CustomerID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14606.0</th>\n",
       "      <td>88.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>135.890114</td>\n",
       "      <td>0.200966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15311.0</th>\n",
       "      <td>89.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>677.729438</td>\n",
       "      <td>0.203229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17841.0</th>\n",
       "      <td>111.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>364.452162</td>\n",
       "      <td>0.253003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12748.0</th>\n",
       "      <td>113.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>298.360885</td>\n",
       "      <td>0.257528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14911.0</th>\n",
       "      <td>131.0</td>\n",
       "      <td>372.0</td>\n",
       "      <td>373.0</td>\n",
       "      <td>1093.661679</td>\n",
       "      <td>0.298252</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            frequency  recency      T  monetary_value  predicted_purchases\n",
       "CustomerID                                                                \n",
       "14606.0          88.0    372.0  373.0      135.890114             0.200966\n",
       "15311.0          89.0    373.0  373.0      677.729438             0.203229\n",
       "17841.0         111.0    372.0  373.0      364.452162             0.253003\n",
       "12748.0         113.0    373.0  373.0      298.360885             0.257528\n",
       "14911.0         131.0    372.0  373.0     1093.661679             0.298252"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "data['predicted_purchases'] = bgf.conditional_expected_number_of_purchases_up_to_time(t, data['frequency'], data['recency'], data['T'])\n",
    "data.sort_values(by='predicted_purchases').tail(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11a024898>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ShIiIJFKCEBGRRBqLSaQNyvee2uvt8nBe02ssqdahqAnCzDoCtwB9gc7AhcA/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\nSCIlCBERSaQEISIiif4fjjLsg1IwMCwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aaa13c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_period_transactions\n",
    "plot_period_transactions(bgf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            frequency_cal  recency_cal  T_cal  frequency_holdout  \\\n",
      "CustomerID                                                         \n",
      "12346.0               0.0          0.0  141.0                0.0   \n",
      "12347.0               2.0        121.0  183.0                4.0   \n",
      "12348.0               2.0        110.0  174.0                1.0   \n",
      "12350.0               0.0          0.0  126.0                0.0   \n",
      "12352.0               3.0         34.0  112.0                3.0   \n",
      "\n",
      "            duration_holdout  \n",
      "CustomerID                    \n",
      "12346.0                  184  \n",
      "12347.0                  184  \n",
      "12348.0                  184  \n",
      "12350.0                  184  \n",
      "12352.0                  184  \n"
     ]
    }
   ],
   "source": [
    "from lifetimes.utils import calibration_and_holdout_data\n",
    "\n",
    "summary_cal_holdout = calibration_and_holdout_data(df, 'CustomerID', 'InvoiceDate',\n",
    "                                        calibration_period_end='2011-06-08',\n",
    "                                        observation_period_end='2011-12-9' )   \n",
    "print(summary_cal_holdout.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11b99e128>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hGkx+URlvLTCH8Z0ztS9t/BplHtR658rdghyl1NlPp6ZqrZv/dYsQ4rz2yzC+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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9a7be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_calibration_purchases_vs_holdout_purchases\n",
    "\n",
    "bgf.fit(summary_cal_holdout['frequency_cal'], summary_cal_holdout['recency_cal'], summary_cal_holdout['T_cal'])\n",
    "plot_calibration_purchases_vs_holdout_purchases(bgf, summary_cal_holdout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1572775101289126"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 10 #predict purchases in 10 periods\n",
    "individual = data.loc[12347]\n",
    "# The below function is an alias to `bfg.conditional_expected_number_of_purchases_up_to_time`\n",
    "bgf.predict(t, individual['frequency'], individual['recency'], individual['T'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "frequency                6.000000\n",
       "recency                365.000000\n",
       "T                      367.000000\n",
       "monetary_value         599.701667\n",
       "predicted_purchases      0.015657\n",
       "Name: 12347.0, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[12347]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11aaa14a8>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LTBBVA8Ys6uCEapAwCy/ojYSVqm63FaYH8TgXA2Q2CnlrcyDxzAeVapYkyU5B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AszVN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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bf9f9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from lifetimes.plotting import plot_history_alive\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "id = 14606\n",
    "days_since_birth = 365\n",
    "sp_trans = df.loc[df['CustomerID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'InvoiceDate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11a032940>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iMzjnrDVVY8h1nCVJkgptixughBCeAFwMHAjcBrwnxrhyk9Mm3AilY+ZsbpPC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cb28160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "id = 14729\n",
    "days_since_birth = 365\n",
    "sp_trans = df.loc[df['CustomerID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'InvoiceDate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            frequency  recency      T  monetary_value  predicted_purchases\n",
      "CustomerID                                                                \n",
      "12347.0           6.0    365.0  367.0      599.701667             0.015657\n",
      "12348.0           3.0    283.0  358.0      301.480000             0.008960\n",
      "12352.0           6.0    260.0  296.0      368.256667             0.018701\n",
      "12356.0           2.0    303.0  325.0      269.905000             0.007173\n",
      "12358.0           1.0    149.0  150.0      683.200000             0.008339\n",
      "2790\n"
     ]
    }
   ],
   "source": [
    "returning_customers_summary = data[data['frequency']>0]\n",
    "\n",
    "print(returning_customers_summary.head())\n",
    "print(len(returning_customers_summary))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>monetary_value</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.015882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>frequency</th>\n",
       "      <td>0.015882</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                monetary_value  frequency\n",
       "monetary_value        1.000000   0.015882\n",
       "frequency             0.015882   1.000000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returning_customers_summary[['monetary_value', 'frequency']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.GammaGammaFitter: fitted with 2790 subjects, p: 2.10, q: 3.45, v: 485.57>\n"
     ]
    }
   ],
   "source": [
    "from lifetimes import GammaGammaFitter\n",
    "\n",
    "ggf = GammaGammaFitter(penalizer_coef = 0)\n",
    "ggf.fit(returning_customers_summary['frequency'],\n",
    "        returning_customers_summary['monetary_value'])\n",
    "print(ggf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CustomerID\n",
      "12346.0    416.917686\n",
      "12347.0    569.988813\n",
      "12348.0    333.762675\n",
      "12349.0    416.917686\n",
      "12350.0    416.917686\n",
      "12352.0    376.166866\n",
      "12353.0    416.917686\n",
      "12354.0    416.917686\n",
      "12355.0    416.917686\n",
      "12356.0    324.008944\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(ggf.conditional_expected_average_profit(\n",
    "        data['frequency'],\n",
    "        data['monetary_value']\n",
    "    ).head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CustomerID\n",
      "12346.0     295.432030\n",
      "12347.0    3012.780611\n",
      "12348.0    1009.518124\n",
      "12349.0    1337.386132\n",
      "12350.0     307.122293\n",
      "12352.0    2374.795598\n",
      "12353.0     426.341427\n",
      "12354.0     386.690293\n",
      "12355.0     411.279755\n",
      "12356.0     784.613969\n",
      "Name: clv, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "bgf.fit(data['frequency'], data['recency'], data['T'])\n",
    "\n",
    "print(ggf.customer_lifetime_value(\n",
    "    bgf, #the model to use to predict the number of future transactions\n",
    "    data['frequency'],\n",
    "    data['recency'],\n",
    "    data['T'],\n",
    "    data['monetary_value'],\n",
    "    time=12, # months\n",
    "    discount_rate=0.01 # monthly discount rate ~ 12.7% annually\n",
    ").head(10))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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